Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.EQ.1

TRIG.91 Solve basic trigonometric equations on intervals Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.91 Solve basic trigonometric equations on intervals. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

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.

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.91 Solve basic trigonometric equations on intervals skill assessments:

Problem 1Difficulty: Mastery

In the interval (-pi, pi], which values of x solve 2cos(4x + pi/4) - sqrt(2) = 0?

A{-5pi/8, -pi/2, -pi/8, 0, 3pi/8, pi/2, 7pi/8, pi}

B{-15pi/16, -11pi/16, -7pi/16, -3pi/16, pi/16, 5pi/16, 9pi/16, 13pi/16}

C{-47pi/48, -31pi/48, -23pi/48, -7pi/48, pi/48, 17pi/48, 25pi/48, 41pi/48}

D{-43pi/48, -35pi/48, -19pi/48, -11pi/48, 5pi/48, 13pi/48, 29pi/48, 37pi/48}

Solution & Explanation:Rewrite the equation as cos(4x + pi/4) = sqrt(2)/2. Use the unit circle and the period of cos to test angles in (-pi, pi]. The values that satisfy the equation in that interval are {-5pi/8, -pi/2, -pi/8, 0, 3pi/8, pi/2, 7pi/8, pi}.

Problem 2Difficulty: Mastery

Determine the complete solution set of 2sin(2x - pi/6) + sqrt(3) = 0 for x in [-2pi, 2pi).

A{-23pi/12, -17pi/12, -11pi/12, -5pi/12, pi/12, 7pi/12, 13pi/12, 19pi/12}

B{-5pi/4, -13pi/12, -pi/4, -pi/12, 3pi/4, 11pi/12, 7pi/4, 23pi/12}

C{-11pi/6, -3pi/2, -5pi/6, -pi/2, pi/6, pi/2, 7pi/6, 3pi/2}

D{-2pi, -4pi/3, -pi, -pi/3, 0, 2pi/3, pi, 5pi/3}

Solution & Explanation:Rewrite the equation as sin(2x - pi/6) = -sqrt(3)/2. Use the unit circle and the period of sin to test angles in [-2pi, 2pi). The values that satisfy the equation in that interval are {-5pi/4, -13pi/12, -pi/4, -pi/12, 3pi/4, 11pi/12, 7pi/4, 23pi/12}.

Problem 3Difficulty: Mastery

For [-pi, pi), what is the complete set of solutions to tan(x/2 + pi/3) = 0?

A{-pi/6}

B{5pi/6}

C{0}

D{-2pi/3}

Solution & Explanation:Use the unit circle and the period of tan to test angles in [-pi, pi). The values that satisfy the equation in that interval are {-2pi/3}.

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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.EQ.1 (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.).