Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.UC.1

TRIG.38 Trigonometric functions defined by the unit circle Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.38 Trigonometric functions defined by the unit circle. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.38 Trigonometric functions defined by the unit circle - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.1. Skill statement in this prompt cell: Select the correct unit-circle definition of sine, cosine, tangent, or a reciprocal trigonometric function for a real-number input. Associated standards listed with this skill in this prompt cell: UTRI.UC.1; CCSS HSF.TF.A.2; FL MA.912.T.2.1-2.2; VA T.CT.2b; NY AII-F.TF.1-2. 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.38 Trigonometric functions defined by the unit circle skill assessments:

Problem 1Difficulty: Mastery
For P(t)=(x, y) with x and y nonzero, which statement correctly compares sec(t) and csc(t)?
Asec(t)=1/x and csc(t)=1/y, so they are reciprocal coordinate functions
Bsec(t)=x/y and csc(t)=y/x, so they are reciprocal ratio functions
Csec(t)=x and csc(t)=y, so they are coordinate functions
Dsec(t)=1/y and csc(t)=1/x, so secant uses the sine coordinate
Solution & Explanation:Secant is reciprocal cosine, which uses x. Cosecant is reciprocal sine, which uses y.
Problem 2Difficulty: Mastery
Which formula set makes cotangent undefined exactly when sine is 0?
Asin(t)=x and cot(t)=y/x
Bsin(t)=1/y and cot(t)=1/x
Csin(t)=y and cot(t)=x/y
Dsin(t)=x/y and cot(t)=y/x
Solution & Explanation:Sine is y. Cotangent is x/y, so cotangent is undefined when y=0, exactly when sin(t)=0.
Problem 3Difficulty: Mastery
Which formula set makes tangent undefined exactly when cosine is 0?
Acos(t)=x and tan(t)=y/x
Bcos(t)=y and tan(t)=x/y
Ccos(t)=1/x and tan(t)=x/y
Dcos(t)=y/x and tan(t)=1/y
Solution & Explanation:Cosine is x. Tangent is y/x, so tangent is undefined when x=0, exactly when cos(t)=0.

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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.1 (Primary standard selected for prompt fields in this prompt cell: UTRI.UC.1. Skill statement in this prompt cell: Select the correct unit-circle definition of sine, cosine, tangent, or a reciprocal trigonometric function for a real-number input. Associated standards listed with this skill in this prompt cell: UTRI.UC.1; CCSS HSF.TF.A.2; FL MA.912.T.2.1-2.2; VA T.CT.2b; NY AII-F.TF.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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