Free Printable WorksheetMathTrigonometryMath CurriculumTRIG.90

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

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.90 Use identities to rewrite and compare sinusoidal models. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

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

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.90 Use identities to rewrite and compare sinusoidal models skill assessments:

Problem 1Difficulty: Mastery

Context: A cosine model is rewritten as sine after subtracting 10pi from the phase. | Model 1: f(t) = 3cos(2t - 21pi/2) + 8 | Model 2: g(t) = 3sin(2t) + 8 | Which identity chain is correct?

Acos(2t - 21pi/2) = -sin(2t)

Bcos(2t - 21pi/2) = cos(2t + pi/2) = -sin(2t)

Csin(2t - 21pi/2) = sin(2t)

Dcos(2t - 21pi/2) = cos(2t - pi/2) = sin(2t)

Solution & Explanation:Focus on the trig part of Model 1. Apply the identity: cos(2t - 21pi/2) = cos(2t - pi/2) = sin(2t). Substitute the rewritten trig term back into Model 1. The remaining coefficients and constant term are identical to Model 2, so the models are equivalent.

Problem 2Difficulty: Mastery

Context: A model converts a sine with -3pi/2 shift to a cosine. | Model 1: f(t) = 6sin(5t - 3pi/2) - 2 | Model 2: g(t) = 6cos(5t) - 2 | Which identity chain is correct?

Acos(5t - 3pi/2) = cos(5t)

Bsin(5t - 3pi/2) = -cos(5t)

Csin(5t - 3pi/2) = sin(5t + pi/2) = cos(5t)

Dsin(5t - 3pi/2) = sin(5t - pi/2) = -cos(5t)

Solution & Explanation:Focus on the trig part of Model 1. Apply the identity: sin(5t - 3pi/2) = sin(5t + pi/2) = cos(5t). Substitute the rewritten trig term back into Model 1. The remaining coefficients and constant term are identical to Model 2, so the models are equivalent.

Problem 3Difficulty: Mastery

Context: A model converts a cosine with 3pi/2 shift to a sine. | Model 1: f(x) = 4cos(7x + 3pi/2) + 1 | Model 2: g(x) = 4sin(7x) + 1 | Which identity chain is correct?

Acos(7x + 3pi/2) = -sin(7x)

Bcos(7x + 3pi/2) = cos(7x - pi/2) = sin(7x)

Ccos(7x + 3pi/2) = cos(7x + pi/2) = -sin(7x)

Dsin(7x + 3pi/2) = sin(7x)

Solution & Explanation:Focus on the trig part of Model 1. Apply the identity: cos(7x + 3pi/2) = cos(7x - pi/2) = sin(7x). Substitute the rewritten trig term back into Model 1. The remaining coefficients and constant term are identical to Model 2, so the models are equivalent.

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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 TRIG.90 (Use identities to rewrite and compare sinusoidal models).