Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.UC.3

TRIG.51 Compare trigonometric values using unit circle reasoning Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.51 Compare trigonometric values using unit circle reasoning. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

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.

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.51 Compare trigonometric values using unit circle reasoning skill assessments:

Problem 1Difficulty: Mastery
On the unit circle, which trigonometric value is greater, cos(23pi/6) or sin(19pi/6)?
Acos(23pi/6) > sin(19pi/6)
Bsin(19pi/6) > cos(23pi/6)
Ccos(23pi/6) = sin(19pi/6)
DBoth values are undefined
Solution & Explanation:On the unit circle, cos(23pi/6) = sqrt(3)/2 and sin(19pi/6) = -1/2 after using the quadrant and reference angle. Since sqrt(3)/2 > -1/2, cos(23pi/6) > sin(19pi/6).
Problem 2Difficulty: Mastery
Compare these two unit-circle values: csc(19pi/6) and cot(11pi/3). Which option gives the correct order?
Acsc(19pi/6) > cot(11pi/3)
Bcot(11pi/3) > csc(19pi/6)
Ccsc(19pi/6) = cot(11pi/3)
DBoth values are undefined
Solution & Explanation:On the unit circle, csc(19pi/6) = -2 and cot(11pi/3) = -sqrt(3)/3 after using the quadrant and reference angle. Since -2 < -sqrt(3)/3, cot(11pi/3) > csc(19pi/6).
Problem 3Difficulty: Mastery
Without using a calculator, decide which value is larger: tan(17pi/4) or sec(13pi/6).
Atan(17pi/4) > sec(13pi/6)
Bsec(13pi/6) > tan(17pi/4)
Ctan(17pi/4) = sec(13pi/6)
DBoth values are undefined
Solution & Explanation:On the unit circle, tan(17pi/4) = 1 and sec(13pi/6) = 2*sqrt(3)/3 after using the quadrant and reference angle. Since 1 < 2*sqrt(3)/3, sec(13pi/6) > tan(17pi/4).

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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.UC.3 (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.).

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