Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.UC.4

TRIG.41 Relationships among all six 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.41 Relationships among all six trigonometric functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.41 Relationships among all six trigonometric functions - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.4. Skill statement in this prompt cell: Determine the remaining trigonometric functions given one value and a quadrant, or select which functions are undefined for a given angle. Associated standards listed with this skill in this prompt cell: UTRI.UC.4; FL MA.912.T.2.2-2.3; VA T.CT.1g-j; CCSS HSF.TF.A.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.41 Relationships among all six trigonometric functions skill assessments:

Problem 1Difficulty: Mastery
Given csc(theta)=-2 and cot(theta)>0, which pair is correct?
Acos = sqrt(3)/2, tan = -sqrt(3)/3
Bcos = -1/2, tan = sqrt(3)
Ccos = 1/2, tan = -sqrt(3)
Dcos = -sqrt(3)/2, tan = sqrt(3)/3
Solution & Explanation:csc(theta)=-2 gives sin(theta)=-1/2. Positive cotangent means cosine has the same sign as sine, so cosine is negative.
Problem 2Difficulty: Mastery
Given sec(theta)=sqrt(2) and cot(theta)<0, which pair is correct?
Asin = sqrt(2)/2, tan = 1
Bsin = -sqrt(2)/2, tan = 1
Csin = -sqrt(2)/2, tan = -1
Dsin = sqrt(2)/2, tan = -1
Solution & Explanation:Positive secant gives positive cosine. Negative cotangent then makes sine negative, so theta is in Quadrant IV.
Problem 3Difficulty: Mastery
Given cot(theta)=sqrt(3) and sec(theta)>0, which pair is correct?
Asin = -1/2, tan = sqrt(3)/3
Bsin = 1/2, tan = sqrt(3)/3
Csin = sqrt(3)/2, tan = sqrt(3)
Dsin = -sqrt(3)/2, tan = sqrt(3)
Solution & Explanation:Positive cotangent and positive secant put theta in Quadrant I for this reference angle, so all relevant signs are positive.

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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.4 (Primary standard selected for prompt fields in this prompt cell: UTRI.UC.4. Skill statement in this prompt cell: Determine the remaining trigonometric functions given one value and a quadrant, or select which functions are undefined for a given angle. Associated standards listed with this skill in this prompt cell: UTRI.UC.4; FL MA.912.T.2.2-2.3; VA T.CT.1g-j; CCSS HSF.TF.A.2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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