Free Printable WorksheetMathAlgebra IIMath CurriculumCCSS F-TF.5

ALG2.203 Writing Trig Functions from Graphs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.203 Writing Trig Functions from Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.203 Writing Trig Functions from Graphs - Primary standard selected for prompt fields in this prompt cell: CCSS F-TF.5. Skill statement in this prompt cell: Select the equation, inequality, expression, or function that represents an equation for a sine or cosine graph using amplitude, period, midline, and phase shift as evidence. Associated standards listed with this skill in this prompt cell: CCSS F-TF.5; F-BF.3; CA CCSSM F-TF.5; F-BF.3; MA 2017 F-TF.5; F-BF.3; NY NGLS F-TF.5; F-BF.3; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.203 Writing Trig Functions from Graphs skill assessments:

Problem 1Difficulty: Mastery

The table lists key points read from one cycle of a sinusoidal graph: x = -7pi/12 -> y = 1; x = -17pi/60 -> y = 5; x = pi/60 -> y = 1; x = 19pi/60 -> y = -3; x = 37pi/60 -> y = 1. Which equation represents the graph?

Af(x) = 4 cos((5/3)(x + 7pi/12)) + 1

Bf(x) = 4 sin((5/3)(x + 7pi/12)) + 1

Cf(x) = 4 sin((5/3)(x + 7pi/12)) + 2

Df(x) = 4 sin((5/3)(x + 17pi/60)) + 1

Solution & Explanation:The amplitude is 4 and the midline is y = 1. The period is 6pi/5, so B = 2pi / (6pi/5) = 5/3. The graph shows an increasing midline crossing, so the sine coefficient is positive. It is shifted left 7pi/12, so the matching equation is f(x) = 4 sin((5/3)(x + 7pi/12)) + 1.

Problem 2Difficulty: Mastery

On the graph, consecutive maximum points occur at x = -5pi/12 and x = 13pi/12, and each has y-value 5/2. The midline is y = -2. Which equation represents this graph?

Af(x) = (9/2) cos((4/3)(x + pi/24)) - 2

Bf(x) = (9/2) cos((4/3)(x + 19pi/24)) - 2

Cf(x) = (9/2) cos((4/3)(x + 5pi/12)) - 2

Df(x) = -(9/2) sin((4/3)(x + 5pi/12)) - 2

Solution & Explanation:The amplitude is 9/2 and the midline is y = -2. The period is 3pi/2, so B = 2pi / (3pi/2) = 4/3. The graph shows a maximum at the shifted starting point, so the cosine coefficient is positive. It is shifted left 5pi/12, so the matching equation is f(x) = (9/2) cos((4/3)(x + 5pi/12)) - 2.

Problem 3Difficulty: Mastery

The graph shown includes a midline crossing at (pi/12, 2) moving downward and then a minimum at (25pi/12, -3/2). The curve has period 8pi. Which equation represents the graph?

Af(x) = -(7/2) cos((1/4)(x - pi/12)) + 2

Bf(x) = -(7/2) sin((1/4)(x - pi/12)) + 3

Cf(x) = -(7/2) sin((1/4)(x - 25pi/12)) + 2

Df(x) = -(7/2) sin((1/4)(x - pi/12)) + 2

Solution & Explanation:The amplitude is 7/2 and the midline is y = 2. The period is 8pi, so B = 2pi / (8pi) = 1/4. The graph shows a decreasing midline crossing, so the sine coefficient is negative. It is shifted right pi/12, so the matching equation is f(x) = -(7/2) sin((1/4)(x - pi/12)) + 2.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard CCSS F-TF.5 (Primary standard selected for prompt fields in this prompt cell: CCSS F-TF.5. Skill statement in this prompt cell: Select the equation, inequality, expression, or function that represents an equation for a sine or cosine graph using amplitude, period, midline, and phase shift as evidence. Associated standards listed with this skill in this prompt cell: CCSS F-TF.5; F-BF.3; CA CCSSM F-TF.5; F-BF.3; MA 2017 F-TF.5; F-BF.3; NY NGLS F-TF.5; F-BF.3; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).