Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.AM.3

TRIG.33 Determine reference angles in all quadrants Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.33 Determine reference angles in all quadrants. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.33 Determine reference angles in all quadrants - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.3. Skill statement in this prompt cell: Select the correct reference angle for an angle in any quadrant. Associated standards listed with this skill in this prompt cell: UTRI.AM.3; VA T.CT.1b,d; TEKS §111.42(c)(4)(C). 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.33 Determine reference angles in all quadrants skill assessments:

Problem 1Difficulty: Mastery
After 12 full rotations measured in radians plus 29pi/21, which pair gives the coterminal angle and reference angle?
Astandard angle = 8pi/21, reference angle = 29pi/21
Bstandard angle = 29pi/21, reference angle = 13pi/21
Cstandard angle = 8pi/21, reference angle = 8pi/21
Dstandard angle = 29pi/21, reference angle = 8pi/21
Solution & Explanation:Reduce 533pi/21 modulo 2pi to 29pi/21. Since 29pi/21 is in Quadrant III, the reference angle is 8pi/21.
Problem 2Difficulty: Mastery
After 20 full turns plus 247°, which pair gives the coterminal angle and reference angle?
Astandard angle = 67°, reference angle = 247°
Bstandard angle = 67°, reference angle = 67°
Cstandard angle = 247°, reference angle = 67°
Dstandard angle = 247°, reference angle = 293°
Solution & Explanation:First reduce 7447° to the coterminal angle 247°. Because 247° is in Quadrant III, its reference angle is 67°.
Problem 3Difficulty: Mastery
For theta = -8pi - 35pi/18, what is the reference angle?
A17pi/18
Bpi/18
C35pi/18
D4pi/9
Solution & Explanation:Reduce -179pi/18 modulo 2pi to get the coterminal angle pi/18, which lies in Quadrant I. In Quadrant I, the reference angle equals the angle, so it is pi/18.

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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.AM.3 (Primary standard selected for prompt fields in this prompt cell: UTRI.AM.3. Skill statement in this prompt cell: Select the correct reference angle for an angle in any quadrant. Associated standards listed with this skill in this prompt cell: UTRI.AM.3; VA T.CT.1b,d; TEKS §111.42(c)(4)(C). Use this prompt-provided wording as the supporting standard description for this workflow.).

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