TRIG.9 Choose a representation that matches the trigonometry situation - Primary standard selected for prompt fields in this prompt cell: UTRI.MP.1-UTRI.MP.5. Skill statement in this prompt cell: Select the representation (diagram, unit circle, graph, table, or identity) that best matches a trigonometry situation and identify the correct translation between representations. Associated standards listed with this skill in this prompt cell: UTRI.MP.1-UTRI.MP.5; CCSS SMP.1-SMP.5; TEKS §111.42(c)(1). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.10 Check solutions using multiple methods - Check solutions using multiple methods

TRIG.11 Interpret units and scales in trigonometric contexts - Interpret units and scales in trigonometric contexts

TRIG.12 Recognize and correct common trigonometry misconceptions - Recognize and correct common trigonometry misconceptions

TRIG.13 Use structure to simplify before computing - Use structure to simplify before computing

TRIG.14 Communicate a complete solution path - Primary standard selected for prompt fields in this prompt cell: UTRI.MP.3. Skill statement in this prompt cell: Select the solution that includes a complete and logically ordered set of steps, with appropriate references to diagrams or graphs. Associated standards listed with this skill in this prompt cell: UTRI.MP.3, UTRI.MP.6; CCSS SMP.3,SMP.6; UTRI.DL.1. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.15 Use similarity and proportional reasoning to compare triangles - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.A.2-3. Skill statement in this prompt cell: Identify whether two triangles are similar and select the correct proportion or scale factor that matches corresponding sides. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.A.2-3; CCSS HSG.SRT.B.4; CCSS HSG.SRT.C.6-8; CCSS HSN.RN.A.2; CCSS HSA.REI.A.1; TEKS §111.42(c)(1). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.16 Apply the Pythagorean theorem and distance formula as trigonometry foundations - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.A.2-3. Skill statement in this prompt cell: Determine the missing side length or distance using the Pythagorean theorem or distance formula, or select whether a triangle is right. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.A.2-3; CCSS HSG.SRT.B.4; CCSS HSG.SRT.C.6-8; CCSS HSN.RN.A.2; CCSS HSA.REI.A.1; TEKS §111.42(c)(1). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.17 Use special right triangles as a basis for exact values - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.B.4. Skill statement in this prompt cell: Select the correct side-length relationship or exact value that comes from a 45-45-90 or 30-60-90 triangle. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.B.4; CCSS HSF.TF.A.3 (+); TEKS §111.42(c)(4)(E); VA T.TT.1b. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.18 Simplify radicals and rational exponents used in exact trigonometry - Simplify radicals and rational exponents used in exact trigonometry

TRIG.19 Solve and rearrange algebraic equations that arise in trigonometry - Solve and rearrange algebraic equations that arise in trigonometry

TRIG.20 Work with function notation and graphs as prerequisites for trigonometry - Primary standard selected for prompt fields in this prompt cell: CCSS HSF.IF.A.1. Skill statement in this prompt cell: Identify function values, domain, range, and key graph features that support later trigonometric graph interpretation. Associated standards listed with this skill in this prompt cell: CCSS HSF.IF.A.1; CCSS HSF.IF.B.4; TEKS §111.42(c)(2)(A). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.21 Identify opposite, adjacent, and hypotenuse relative to a reference angle - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.C.6. Skill statement in this prompt cell: Select which side is opposite, adjacent, or hypotenuse relative to a marked angle in a right triangle. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.C.6; FL MA.912.T.1.1; VA T.TT.1a. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.22 Use algebra to solve a proportion that represents a trigonometric ratio - Use algebra to solve a proportion that represents a trigonometric ratio

TRIG.23 Distinguish exact values from approximations and choose appropriately - Distinguish exact values from approximations and choose appropriately

TRIG.24 Use a coordinate grid to represent geometric information - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.GPE.B.4. Skill statement in this prompt cell: Select the correct plotted point, distance, or slope interpretation on a coordinate grid for a geometry or trigonometry setup. Associated standards listed with this skill in this prompt cell: CCSS HSG.GPE.B.4; CCSS HSG.SRT.C.8; TEKS §111.42(c)(4). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.25 Interpret angle relationships used in trigonometry - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.C.7. Skill statement in this prompt cell: Identify complementary or supplementary relationships in an angle diagram and select the related trigonometric relationship that follows. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.C.7; UTRI.ID.2; VA T.CT.1f. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.26 Set calculator or software to the correct angle mode - Set calculator or software to the correct angle mode

TRIG.27 Angle measure in degrees and radians - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.1. Skill statement in this prompt cell: Select the correct definition of a radian and identify equivalent degree and radian measures for a given rotation, including negative angles. Associated standards listed with this skill in this prompt cell: UTRI.AM.1; CCSS HSF.TF.A.1; VA T.CT.1a-b; TEKS §111.42(c)(4)(B)-(D). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.28 Arc length and sector area - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.2. Skill statement in this prompt cell: Determine arc length or sector area, or select the correct formula and substitution (using radians) for a given circle situation. Associated standards listed with this skill in this prompt cell: UTRI.AM.2; CCSS HSG.C.B.5; TEKS §111.41(c)(12)(B)-(C); FL MA.912.GR.6.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.29 Reference angles and coterminal angles - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.3. Skill statement in this prompt cell: Select the correct coterminal angle, reference angle, or quadrant for a given angle in standard position. Associated standards listed with this skill in this prompt cell: UTRI.AM.3; VA T.CT.1b,d; TEKS §111.42(c)(4)(C). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.30 Convert between degrees and radians with and without a calculator - Convert between degrees and radians with and without a calculator

TRIG.31 Interpret radians as a ratio and as an arc length - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.1. Skill statement in this prompt cell: Select the statement that correctly interprets radians as arc length per radius and connects to s = r theta. Associated standards listed with this skill in this prompt cell: UTRI.AM.1; CCSS HSF.TF.A.1; VA T.CT.1a-b; TEKS §111.42(c)(4)(B)-(D). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.32 Find coterminal angles and determine standard-position equivalents - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.3. Skill statement in this prompt cell: Determine an angle coterminal with a given angle that lies in a specified interval such as [0, 2π) or (-π, π]. Associated standards listed with this skill in this prompt cell: UTRI.AM.3; VA T.CT.1b,d; TEKS §111.42(c)(4)(C). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.33 Determine reference angles in all quadrants - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.3. Skill statement in this prompt cell: Select the correct reference angle for an angle in any quadrant. Associated standards listed with this skill in this prompt cell: UTRI.AM.3; VA T.CT.1b,d; TEKS §111.42(c)(4)(C). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.34 Compute arc length from radius and central angle - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.2. Skill statement in this prompt cell: Select the correct arc length given radius and central angle, including solving for a missing variable when needed. Associated standards listed with this skill in this prompt cell: UTRI.AM.2; CCSS HSG.C.B.5; TEKS §111.41(c)(12)(B)-(C); FL MA.912.GR.6.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.35 Compute sector area from radius and central angle - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.2. Skill statement in this prompt cell: Select the correct sector area given radius and central angle, including solving for a missing variable when needed. Associated standards listed with this skill in this prompt cell: UTRI.AM.2; CCSS HSG.C.B.5; TEKS §111.41(c)(12)(B)-(C); FL MA.912.GR.6.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.36 Solve problems involving angular speed and linear speed - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.1. Skill statement in this prompt cell: Determine linear speed or angular speed from v = rω or s = rθ and select the answer with correct units. Associated standards listed with this skill in this prompt cell: UTRI.AM.1; CCSS HSF.TF.A.1; VA T.CT.1a-b; TEKS §111.42(c)(4)(B)-(D); TEKS §111.42(c)(4)(D). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.37 Represent rotations and angles on a diagram and coordinate plane - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.3. Skill statement in this prompt cell: Select the correct diagram or coordinate representation of an angle in standard position, including direction of rotation. Associated standards listed with this skill in this prompt cell: UTRI.AM.3; VA T.CT.1b,d; TEKS §111.42(c)(4)(C). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.38 Trigonometric functions defined by the unit circle - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.1. Skill statement in this prompt cell: Select the correct unit-circle definition of sine, cosine, tangent, or a reciprocal trigonometric function for a real-number input. Associated standards listed with this skill in this prompt cell: UTRI.UC.1; CCSS HSF.TF.A.2; FL MA.912.T.2.1-2.2; VA T.CT.2b; NY AII-F.TF.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.39 Special angles and exact trigonometric values - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.2. Skill statement in this prompt cell: Select the exact value of sine, cosine, or tangent at a special angle (in radians) using unit-circle or special-triangle reasoning. Associated standards listed with this skill in this prompt cell: UTRI.UC.2; CCSS HSF.TF.A.3 (+); FL MA.912.T.2.1; VA T.CT.2c. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.40 Symmetry and periodicity of trigonometric functions - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.3. Skill statement in this prompt cell: Identify the correct symmetry, even or odd property, or period that rewrites a trigonometric expression into an equivalent simpler form. Associated standards listed with this skill in this prompt cell: UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.41 Relationships among all six trigonometric functions - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.4. Skill statement in this prompt cell: Determine the remaining trigonometric functions given one value and a quadrant, or select which functions are undefined for a given angle. Associated standards listed with this skill in this prompt cell: UTRI.UC.4; FL MA.912.T.2.2-2.3; VA T.CT.1g-j; CCSS HSF.TF.A.2. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.42 Identify unit-circle coordinates for key quadrantal angles - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.1. Skill statement in this prompt cell: Select the coordinate pair (cosine, sine) for a key quadrantal angle and identify which coordinate corresponds to which function. Associated standards listed with this skill in this prompt cell: UTRI.UC.1; CCSS HSF.TF.A.2; FL MA.912.T.2.1-2.2; VA T.CT.2b; NY AII-F.TF.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.43 Use reference angles and quadrants to determine signs - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.3. Skill statement in this prompt cell: Select the correct sign of sine, cosine, and tangent for a given quadrant and apply it to an exact value. Associated standards listed with this skill in this prompt cell: UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.44 Evaluate sine, cosine, and tangent using special triangles - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.2. Skill statement in this prompt cell: Select the correct exact value of sine, cosine, or tangent for 30 degrees, 45 degrees, 60 degrees (or π/6, π/4, π/3) using special triangles. Associated standards listed with this skill in this prompt cell: UTRI.UC.2; CCSS HSF.TF.A.3 (+); FL MA.912.T.2.1; VA T.CT.2c. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.45 Find trig values for angles outside the first quadrant - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.2. Skill statement in this prompt cell: Select the equivalent reference-angle expression (using periodicity or symmetry) and determine the correct trig value. Associated standards listed with this skill in this prompt cell: UTRI.UC.2; CCSS HSF.TF.A.3 (+); FL MA.912.T.2.1; VA T.CT.2c; UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.46 Compute secant, cosecant, and cotangent from sine, cosine, and tangent - Compute secant, cosecant, and cotangent from sine, cosine, and tangent

TRIG.47 Determine all six trig functions from one function value and quadrant - Determine all six trig functions from one function value and quadrant

TRIG.48 Use the Pythagorean identity to connect sine and cosine values - Use the Pythagorean identity to connect sine and cosine values

TRIG.49 Use cofunction relationships for complementary angles - Use cofunction relationships for complementary angles

TRIG.50 Find all angles in an interval with a given trig value - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select all angles in a specified interval that satisfy a given sine, cosine, or tangent value. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a; UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.51 Compare trigonometric values using unit-circle reasoning - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.3. Skill statement in this prompt cell: Select which of two trigonometric values is larger based on unit-circle reasoning (quadrant and reference angle). Associated standards listed with this skill in this prompt cell: UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.52 Recognize the ranges of sine and cosine and constraints on values - Recognize the ranges of sine and cosine and constraints on values

TRIG.53 Connect the unit circle to sine and cosine graphs - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.1. Skill statement in this prompt cell: Select the graph feature or plotted point that corresponds to a given unit-circle position and vice versa. Associated standards listed with this skill in this prompt cell: UTRI.GT.1; VA T.GT.1a-b; TEKS §111.42(c)(2)(F)-(J); FL MA.912.T.3.4; UTRI.UC.1; CCSS HSF.TF.A.2; FL MA.912.T.2.1-2.2; VA T.CT.2b; NY AII-F.TF.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.54 Parent graphs of trigonometric functions - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.1. Skill statement in this prompt cell: Select the correct parent graph for a given trigonometric function and identify key features such as intercepts, extrema, period, and asymptotes. Associated standards listed with this skill in this prompt cell: UTRI.GT.1; VA T.GT.1a-b; TEKS §111.42(c)(2)(F)-(J); FL MA.912.T.3.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.55 Transformations and parameters of trigonometric functions - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Determine how parameters A, B, C, and D change a trigonometric graph and select the transformed graph or equation that matches those parameters. Associated standards listed with this skill in this prompt cell: UTRI.GT.2; CCSS HSF.TF.B.5; VA T.GT.1c-d; NY AII-F.BF.3; TEKS §111.42(c)(2)(G). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.56 Model periodic phenomena with trigonometric functions - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.3. Skill statement in this prompt cell: Select the trigonometric model that best fits a periodic context or dataset and identify the meaning of its parameters and domain. Associated standards listed with this skill in this prompt cell: UTRI.GT.3; CCSS HSF.TF.B.5; FL MA.912.T.3.3,3.5; VA T.GT.1e. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.57 Inverse trigonometric functions and inverse graphs - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.4. Skill statement in this prompt cell: Identify the correct restricted domain and range for an inverse trig function and select the correct inverse graph as a reflection across y = x. Associated standards listed with this skill in this prompt cell: UTRI.GT.4; CCSS HSF.TF.B.6; VA T.GT.2; FL MA.912.T.3.6. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.58 Identify period, amplitude, midline, and phase shift from a graph - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Determine period, amplitude, midline, and phase shift from a displayed sinusoidal graph. Associated standards listed with this skill in this prompt cell: UTRI.GT.2; CCSS HSF.TF.B.5; VA T.GT.1c-d; NY AII-F.BF.3; TEKS §111.42(c)(2)(G). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.59 Graph a transformed sine or cosine function from an equation - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Select the correct graph of a given transformed sine or cosine equation, including key points for one or more periods. Associated standards listed with this skill in this prompt cell: UTRI.GT.2; CCSS HSF.TF.B.5; VA T.GT.1c-d; NY AII-F.BF.3; TEKS §111.42(c)(2)(G). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.60 Write an equation for a sinusoidal function from key features - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Select the equation that matches a given sinusoidal graph, table, or context using amplitude, period, phase shift, and midline. Associated standards listed with this skill in this prompt cell: UTRI.GT.2; CCSS HSF.TF.B.5; VA T.GT.1c-d; NY AII-F.BF.3; TEKS §111.42(c)(2)(G); UTRI.GT.3; CCSS HSF.TF.B.5; FL MA.912.T.3.3,3.5; VA T.GT.1e. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.61 Interpret real-world meaning of sinusoidal parameters - Interpret real-world meaning of sinusoidal parameters

TRIG.62 Identify and interpret asymptotes for tangent, secant, cosecant, and cotangent - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.1. Skill statement in this prompt cell: Identify the correct locations of vertical asymptotes for tangent, cotangent, secant, or cosecant and select the correct domain exclusions. Associated standards listed with this skill in this prompt cell: UTRI.GT.1; VA T.GT.1a-b; TEKS §111.42(c)(2)(F)-(J); FL MA.912.T.3.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.63 Determine domain and range from trigonometric graphs - Determine domain and range from trigonometric graphs

TRIG.64 Restrict the domain of a trig function to make it invertible - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.4. Skill statement in this prompt cell: Select an interval on which sine, cosine, or tangent is one-to-one and identify the resulting range of the inverse. Associated standards listed with this skill in this prompt cell: UTRI.GT.4; CCSS HSF.TF.B.6; VA T.GT.2; FL MA.912.T.3.6. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.65 Evaluate inverse trigonometric functions using special values and approximations - Evaluate inverse trigonometric functions using special values and approximations

TRIG.66 Compose trigonometric and inverse trigonometric functions with domain awareness - Compose trigonometric and inverse trigonometric functions with domain awareness

TRIG.67 Use technology to verify graphs and explore parameter changes - Primary standard selected for prompt fields in this prompt cell: UTRI.MP.5. Skill statement in this prompt cell: Select the correct technology settings (mode, window, table) and identify the correct conclusion from graphing or table output when parameters change. Associated standards listed with this skill in this prompt cell: UTRI.MP.5; CCSS SMP.5; TEKS §111.42(c)(1)(C); FL MA.912.T.3.7; ISTE Students 1-7; UTRI.GT.2; CCSS HSF.TF.B.5; VA T.GT.1c-d; NY AII-F.BF.3; TEKS §111.42(c)(2)(G). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.68 Fit a sinusoidal model to data using key points - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.3. Skill statement in this prompt cell: Select amplitude, period, phase shift, and midline that fit key data features and choose the best matching sinusoidal equation. Associated standards listed with this skill in this prompt cell: UTRI.GT.3; CCSS HSF.TF.B.5; FL MA.912.T.3.3,3.5; VA T.GT.1e. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.69 Evaluate the reasonableness and limitations of a periodic model - Evaluate the reasonableness and limitations of a periodic model

TRIG.70 Convert between sine and cosine models using phase shifts - Convert between sine and cosine models using phase shifts

TRIG.71 Use trigonometric graphs to estimate solutions to equations and inequalities - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select approximate solution values for a trigonometric equation or inequality based on graph intersections and behavior. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a; UTRI.GT.1; VA T.GT.1a-b; TEKS §111.42(c)(2)(F)-(J); FL MA.912.T.3.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.72 Pythagorean, reciprocal, and quotient identities - Pythagorean, reciprocal, and quotient identities

TRIG.73 Even, odd, and cofunction identities - Even, odd, and cofunction identities

TRIG.74 Sum and difference identities - Sum and difference identities

TRIG.75 Double-angle and half-angle identities - Double-angle and half-angle identities

TRIG.76 Verifying identities and writing clear proofs - Verifying identities and writing clear proofs

TRIG.77 Rewrite an expression using only sine and cosine - Rewrite an expression using only sine and cosine

TRIG.78 Use identities to simplify complex rational trigonometric expressions - Use identities to simplify complex rational trigonometric expressions

TRIG.79 Determine missing trig values using identities and quadrant information - Determine missing trig values using identities and quadrant information

TRIG.80 Use even and odd identities to evaluate functions of negative angles - Use even and odd identities to evaluate functions of negative angles

TRIG.81 Use cofunction identities to connect complementary angles - Use cofunction identities to connect complementary angles

TRIG.82 Apply sum and difference identities to compute exact values - Apply sum and difference identities to compute exact values

TRIG.83 Use sum and difference identities to transform expressions - Use sum and difference identities to transform expressions

TRIG.84 Apply double-angle identities to simplify and evaluate - Apply double-angle identities to simplify and evaluate

TRIG.85 Apply half-angle identities with correct sign reasoning - Apply half-angle identities with correct sign reasoning

TRIG.86 Select an efficient identity strategy for a given problem - Select an efficient identity strategy for a given problem

TRIG.87 Verify an identity by transforming one side only - Verify an identity by transforming one side only

TRIG.88 Recognize domain restrictions that affect identity use - Recognize domain restrictions that affect identity use

TRIG.89 Check an identity numerically and interpret discrepancies - Check an identity numerically and interpret discrepancies

TRIG.90 Use identities to rewrite and compare sinusoidal models - Use identities to rewrite and compare sinusoidal models

TRIG.91 Solve basic trigonometric equations on intervals - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select the complete set of solutions to a basic trigonometric equation within a given interval. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.92 Solve advanced trigonometric equations using identities and algebra - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.2. Skill statement in this prompt cell: Select the correct solution set for a multi-step trigonometric equation that requires identities, factoring, or inverse functions. Associated standards listed with this skill in this prompt cell: UTRI.EQ.2; CCSS HSF.TF.B.7 (+); TEKS §111.42(c)(5)(N); VA T.IE.3a,c. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.93 Solve trigonometric inequalities and justify solution sets - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.3. Skill statement in this prompt cell: Select the correct union of intervals that satisfies a trigonometric inequality, accounting for periodicity and discontinuities. Associated standards listed with this skill in this prompt cell: UTRI.EQ.3; VA T.IE.3b; CCSS HSF.IF.B.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.94 Find all solutions to sine(x) = k and cosine(x) = k in one cycle - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select all angles in one cycle that satisfy sine(x) = k or cosine(x) = k using reference angles and symmetry. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.95 Find all solutions to tangent(x) = k in a specified interval - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select all angles in the stated interval that satisfy tangent(x) = k using periodicity and domain exclusions. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.96 Write general solutions using periodicity - Write general solutions using periodicity

TRIG.97 Solve equations with linear arguments such as sine(2x - π/3) = 1/2 - Solve equations with linear arguments such as sine 2x minus pi over 3 equals 1 over 2

TRIG.98 Solve equations that require factoring after using identities - Solve equations that require factoring after using identities

TRIG.99 Solve equations involving squared trig functions - Solve equations involving squared trig functions

TRIG.100 Solve equations by converting between sine and cosine using the Pythagorean identity - Solve equations by converting between sine and cosine using the Pythagorean identity

TRIG.101 Use inverse trigonometric functions in modeling contexts - Use inverse trigonometric functions in modeling contexts

TRIG.102 Solve trigonometric inequalities on a given interval - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.3. Skill statement in this prompt cell: Select the correct interval solution for where a trig function is greater than or less than a constant on a given interval. Associated standards listed with this skill in this prompt cell: UTRI.EQ.3; VA T.IE.3b; CCSS HSF.IF.B.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.103 Interpret how asymptotes affect inequality solutions - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.3. Skill statement in this prompt cell: Identify which points must be excluded due to undefined values and select the inequality solution that respects discontinuities. Associated standards listed with this skill in this prompt cell: UTRI.EQ.3; VA T.IE.3b; CCSS HSF.IF.B.4; UTRI.GT.1; VA T.GT.1a-b; TEKS §111.42(c)(2)(F)-(J); FL MA.912.T.3.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.104 Estimate solutions using graphs and confirm algebraically - Primary standard selected for prompt fields in this prompt cell: UTRI.MP.5. Skill statement in this prompt cell: Select an approximate solution from a graph and identify the substitution check that confirms it. Associated standards listed with this skill in this prompt cell: UTRI.MP.5; CCSS SMP.5; TEKS §111.42(c)(1)(C); FL MA.912.T.3.7; ISTE Students 1-7; UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.105 Identify and remove extraneous solutions - Identify and remove extraneous solutions

TRIG.106 Communicate solution sets with clear notation - Communicate solution sets with clear notation

TRIG.107 Determine the number of solutions without fully solving - Determine the number of solutions without fully solving

TRIG.108 Right-triangle trigonometry in applied problems - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.1. Skill statement in this prompt cell: Select the correct trigonometric ratio or inverse-trigonometric method to solve a right-triangle application and identify the correctly rounded answer with units. Associated standards listed with this skill in this prompt cell: UTRI.TA.1; CCSS HSG.SRT.C.6-8; TEKS §111.42(c)(4)(E)-(F); FL MA.912.T.1.1-1.2; VA T.TT.1a,c-d. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.109 Law of Sines and Law of Cosines for general triangles - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select which law applies to a given triangle information set and determine the missing side, angle, or area. Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.110 Vectors in the plane using direction and magnitude - UTRI.TA.3: Select the correct vector representation or operation (addition, scaling, components) to model a navigation or force situation. Associated standards listed with this skill: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted).

TRIG.111 Set up a right-triangle model from a word problem - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.1. Skill statement in this prompt cell: Select the diagram and equation that correctly represent a word problem as a right triangle. Associated standards listed with this skill in this prompt cell: UTRI.TA.1; CCSS HSG.SRT.C.6-8; TEKS §111.42(c)(4)(E)-(F); FL MA.912.T.1.1-1.2; VA T.TT.1a,c-d. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.112 Use inverse trigonometric functions to find angles in right triangles - Use inverse trigonometric functions to find angles in right triangles

TRIG.113 Solve problems involving angles of elevation and depression - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.1. Skill statement in this prompt cell: Select the correct diagram and equation for an elevation or depression problem and determine the unknown distance or height. Associated standards listed with this skill in this prompt cell: UTRI.TA.1; CCSS HSG.SRT.C.6-8; TEKS §111.42(c)(4)(E)-(F); FL MA.912.T.1.1-1.2; VA T.TT.1a,c-d. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.114 Solve bearing and navigation problems with right triangles - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.1. Skill statement in this prompt cell: Select the correct right-triangle or coordinate model for a bearing problem and determine the resultant distance or direction. Associated standards listed with this skill in this prompt cell: UTRI.TA.1; CCSS HSG.SRT.C.6-8; TEKS §111.42(c)(4)(E)-(F); FL MA.912.T.1.1-1.2; VA T.TT.1a,c-d. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.115 Choose between the Law of Sines and Law of Cosines - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select which law of sines or law of cosines is appropriate for given triangle data (ASA, AAS, SAS, SSS, SSA). Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.116 Solve a triangle using the Law of Sines - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select the correct Law of Sines setup and determine the missing side or angle. Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.117 Solve a triangle using the Law of Cosines - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select the correct Law of Cosines setup and determine the missing side or angle. Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.118 Analyze the ambiguous case for the Law of Sines - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select whether SSA yields zero, one, or two triangles and identify the valid solution or solutions. Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.119 Use the trigonometric area formula for a triangle - Primary standard selected for prompt fields in this prompt cell: CCSS HSG.SRT.D.9 (+). Skill statement in this prompt cell: Select the correct area using (1/2)ab sine(C) and identify the included angle in the formula. Associated standards listed with this skill in this prompt cell: CCSS HSG.SRT.D.9 (+); UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.120 Solve multi-step applications involving general triangles - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.2. Skill statement in this prompt cell: Select the correct sequence of steps and computations for a multi-step application involving a general triangle. Associated standards listed with this skill in this prompt cell: UTRI.TA.2; CCSS HSG.SRT.D.10-11 (+); FL MA.912.T.1.3-1.4; VA T.TT.2a-c; TEKS §111.42(c)(4)(G)-(H). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.121 Represent vectors with components and magnitude - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.3. Skill statement in this prompt cell: Select the correct component form, magnitude, or direction-angle representation for a vector. Associated standards listed with this skill in this prompt cell: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.122 Add, subtract, and scale vectors to model resultant quantities - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.3. Skill statement in this prompt cell: Select the resultant vector from addition, subtraction, or scaling and identify the correct magnitude and direction interpretation. Associated standards listed with this skill in this prompt cell: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.123 Resolve a vector into perpendicular components using trigonometry - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.3. Skill statement in this prompt cell: Select the correct horizontal and vertical components using sine and cosine for a given magnitude and direction. Associated standards listed with this skill in this prompt cell: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.124 Check triangle and vector results for validity and reasonableness - Check triangle and vector results for validity and reasonableness

TRIG.125 Polar coordinates and polar graphs - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.1. Skill statement in this prompt cell: Select the correct polar or rectangular representation of a point or equation and identify key features of a polar graph. Associated standards listed with this skill in this prompt cell: UTRI.PPC.1; FL MA.912.T.4.1-4.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.126 Parametric representations of planar motion - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.2. Skill statement in this prompt cell: Select the correct parametric graph or conversion result and identify how the curve is traced as the parameter increases. Associated standards listed with this skill in this prompt cell: UTRI.PPC.2; FL MA.912.T.4.5-4.7. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.127 Complex numbers in polar (trigonometric) form - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.3. Skill statement in this prompt cell: Select the correct polar form of a complex number (modulus and argument) and interpret the argument as a rotation. Associated standards listed with this skill in this prompt cell: UTRI.PPC.3; CCSS HSN.CN.B.4 (+); MA 2017 N-CN (+). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.128 De Moivre's theorem and roots of complex numbers - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.4. Skill statement in this prompt cell: Select the correct result of applying De Moivre's theorem to compute a power or roots and identify the geometric pattern of roots on the complex plane. Associated standards listed with this skill in this prompt cell: UTRI.PPC.4; CCSS HSN.CN.B.5-6 (+). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.129 Convert points between rectangular and polar form - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.1. Skill statement in this prompt cell: Select the correct conversion between rectangular and polar coordinates, including equivalent angles. Associated standards listed with this skill in this prompt cell: UTRI.PPC.1; FL MA.912.T.4.1-4.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.130 Use symmetry and key angles to sketch polar graphs - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.1. Skill statement in this prompt cell: Select the symmetry that applies to a polar equation and choose an effective sketching strategy using key angles. Associated standards listed with this skill in this prompt cell: UTRI.PPC.1; FL MA.912.T.4.1-4.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.131 Recognize and graph common polar curves - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.1. Skill statement in this prompt cell: Select the curve type (circle, line, rose, spiral) that matches a polar equation and identify key shape features. Associated standards listed with this skill in this prompt cell: UTRI.PPC.1; FL MA.912.T.4.1-4.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.132 Use technology to graph and verify polar and parametric equations - Primary standard selected for prompt fields in this prompt cell: UTRI.MP.5. Skill statement in this prompt cell: Select the correct technology mode and settings to graph a polar or parametric equation and identify the correct output. Associated standards listed with this skill in this prompt cell: UTRI.MP.5; UTRI.PPC.1; FL MA.912.T.4.1-4.4. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.133 Interpret a parametric curve's direction and key points - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.2. Skill statement in this prompt cell: Select the starting point and direction of motion for a parametric curve and identify key points for given parameter values. Associated standards listed with this skill in this prompt cell: UTRI.PPC.2; FL MA.912.T.4.5-4.7. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.134 Eliminate the parameter when conversion is feasible - Eliminate the parameter when conversion is feasible

TRIG.135 Convert a complex number to polar form and interpret modulus and argument - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.3. Skill statement in this prompt cell: Select the modulus and argument for a complex number and choose the correct polar-form expression r(cos theta + i sine theta). Associated standards listed with this skill in this prompt cell: UTRI.PPC.3; CCSS HSN.CN.B.4 (+); MA 2017 N-CN (+). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.136 Multiply and divide complex numbers using polar form - Multiply and divide complex numbers using polar form

TRIG.137 Apply De Moivre's theorem to compute powers of complex numbers - Apply De Moivres theorem to compute powers of complex numbers

TRIG.138 Find all n-th roots of a complex number - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.4. Skill statement in this prompt cell: Select all distinct n-th roots of a complex number and identify their equal spacing on the complex plane. Associated standards listed with this skill in this prompt cell: UTRI.PPC.4; CCSS HSN.CN.B.5-6 (+). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.139 Connect Euler’s formula to trigonometric representations - Connect Euler’s formula to trigonometric representations

TRIG.140 Connect polar form, vectors, and trigonometric rotation - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.1. Skill statement in this prompt cell: Select the statement that correctly connects polar magnitude-direction ideas to vectors or rotations. Associated standards listed with this skill in this prompt cell: UTRI.PPC.1; FL MA.912.T.4.1-4.4; UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.141 Mathematical communication in trigonometry - Primary standard selected for prompt fields in this prompt cell: UTRI.DL.1. Skill statement in this prompt cell: Select the solution or explanation that uses correct notation, vocabulary, and multiple representations to justify a trigonometric conclusion. Associated standards listed with this skill in this prompt cell: UTRI.DL.1; CCSS SMP.3,SMP.6; WIDA 2020 Key Language Uses (Argue, Explain, Inform). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.142 Technology and data ethics in trigonometry - Technology and data ethics in trigonometry

TRIG.143 Label graphs and diagrams with units and key features - Primary standard selected for prompt fields in this prompt cell: UTRI.DL.1. Skill statement in this prompt cell: Select the correctly labeled graph or diagram (including units and key features) that supports accurate interpretation. Associated standards listed with this skill in this prompt cell: UTRI.DL.1; CCSS SMP.3,SMP.6; WIDA 2020 Key Language Uses (Argue, Explain, Inform). Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.144 Write solutions that justify each transformation step - Write solutions that justify each transformation step

TRIG.145 Distinguish inverse trigonometric functions from reciprocal functions in writing - Distinguish inverse trigonometric functions from reciprocal functions in writing

TRIG.146 Create a clear modeling report for a sinusoidal situation - Primary standard selected for prompt fields in this prompt cell: UTRI.DL.1. Skill statement in this prompt cell: Select the report element (equation, graph, parameter interpretation, domain, limitation) that makes a periodic-model write-up complete. Associated standards listed with this skill in this prompt cell: UTRI.DL.1; CCSS SMP.3,SMP.6; WIDA 2020 Key Language Uses (Argue, Explain, Inform); UTRI.DL.2; ISTE Students 1-3,6-7. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.147 Use spreadsheets to organize data and compute model outputs - Primary standard selected for prompt fields in this prompt cell: UTRI.DL.2. Skill statement in this prompt cell: Select the spreadsheet setup (formulas, table layout, chart) that correctly computes and displays model predictions. Associated standards listed with this skill in this prompt cell: UTRI.DL.2; ISTE Students 1-3,6-7. Use this prompt-provided wording as the supporting standard description for this workflow.

TRIG.148 Evaluate the reliability of digital sources for data and formulas - Evaluate the reliability of digital sources for data and formulas

TRIG.149 Collaborate and critique mathematically with respect and precision - Collaborate and critique mathematically with respect and precision

TRIG.150 Use technology to present trigonometry work accessibly - Use technology to present trigonometry work accessibly