Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.UC.3

TRIG.43 Use reference angles and quadrants to determine signs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.43 Use reference angles and quadrants to determine signs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.43 Use reference angles and quadrants to determine signs - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.3. Skill statement in this prompt cell: Select the correct sign of sine, cosine, and tangent for a given quadrant and apply it to an exact value. 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.43 Use reference angles and quadrants to determine signs skill assessments:

Problem 1Difficulty: Mastery
The reference angle for theta is pi/3. If cos(theta) > 0 and sin(theta) < 0, what is cos(theta) - tan(theta)?
Asqrt(3) + 1/2
B1/2 - sqrt(3)
Csqrt(3) - 1/2
D-sqrt(3) - 1/2
Solution & Explanation:cos(theta) > 0 and sin(theta) < 0 place theta in Quadrant IV. Cosine is 1/2 and tangent is -sqrt(3), so cos(theta) - tan(theta) = 1/2 + sqrt(3).
Problem 2Difficulty: Mastery
The reference angle for theta is pi/6. If cos(theta) < 0 and sin(theta) < 0, what is tan(theta) + sin(theta)?
Asqrt(3)/3 - 1/2
Bsqrt(3)/3 + 1/2
C-sqrt(3)/3 - 1/2
D1/2 - sqrt(3)/3
Solution & Explanation:cos(theta) < 0 and sin(theta) < 0 place theta in Quadrant III. Tangent is sqrt(3)/3 and sine is -1/2, so the sum is sqrt(3)/3 - 1/2.
Problem 3Difficulty: Mastery
The reference angle for theta is 60 degrees. If sin(theta) > 0 and tan(theta) < 0, what is sin(theta) - cos(theta)?
A(sqrt(3) + 1)/2
B(sqrt(3) - 1)/2
C-(sqrt(3) + 1)/2
Dsqrt(3) - 1/2
Solution & Explanation:sin(theta) > 0 and tan(theta) < 0 place theta in Quadrant II. Then sin(theta) = sqrt(3)/2 and cos(theta) = -1/2, so sin(theta) - cos(theta) = (sqrt(3) + 1)/2.

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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 the correct sign of sine, cosine, and tangent for a given quadrant and apply it to an exact value. 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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