Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.GT.2

TRIG.55 Transformations and parameters of trigonometric functions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.55 Transformations and parameters of trigonometric functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

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.

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

Trigonometry

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 TRIG.55 Transformations and parameters of trigonometric functions skill assessments:

Problem 1Difficulty: Mastery
A buoy height model has maximum 4.2 meters, minimum 1.0 meter, period 6 seconds, and is at the midline rising when t = 1.5. Which equation fits?
Ah(t) = 1.6sin((pi/3)(t - 1.5)) + 2.6
Bh(t) = 2.6sin((pi/3)(t - 1.5)) + 1.6
Ch(t) = 1.6cos((pi/3)(t - 1.5)) + 2.6
Dh(t) = -1.6sin((pi/6)(t - 1.5)) + 2.6
Solution & Explanation:The amplitude is (4.2 - 1.0)/2 = 1.6 and the midline is 2.6. Period 6 gives B = 2pi/6 = pi/3. A sine graph is at the midline rising at t = C, so C = 1.5.
Problem 2Difficulty: Mastery
True or False: In y = A sin(B(x-C)) + D, changing C affects where peaks occur but not the amplitude, period, or midline.
ATrue
BFalse
Solution & Explanation:C shifts the graph horizontally. It moves the x-locations of peaks and troughs, but abs(A), B, and D still determine amplitude, period, and midline.
Problem 3Difficulty: Mastery
For y = A cos(B(x-C)) + D with A > 0, a graph has maximum 11 at x = 2, minimum -5 at x = 7, and next maximum at x = 12. Which values match A, B, C, and D?
AA = 8, B = pi/5, C = 2, D = 3
BA = 8, B = pi/10, C = 7, D = 3
CA = 3, B = pi/5, C = 2, D = 8
DA = -8, B = pi/5, C = 7, D = 3
Solution & Explanation:The amplitude is (11 - (-5))/2 = 8 and the midline is 3. Max to next max gives period 10, so B = 2pi/10 = pi/5. With A > 0, the maximum occurs at C = 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 Trigonometry Math students. It aligns with educational standard UTRI.GT.2 (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.).

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