Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.AM.3

TRIG.32 Find coterminal angles and determine standard position equivalents Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.32 Find coterminal angles and determine standard position equivalents. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.32 Find coterminal angles and determine standard-position equivalents - Primary standard selected for prompt fields in this prompt cell: UTRI.AM.3. Skill statement in this prompt cell: Determine an angle coterminal with a given angle that lies in a specified interval such as [0, 2π) or (-π, π]. 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.32 Find coterminal angles and determine standard position equivalents skill assessments:

Problem 1Difficulty: Mastery
Which angle in [4pi, 6pi) is coterminal with -14pi/3?
A10pi/3
B16pi/3
C22pi/3
D4pi/3
Solution & Explanation:Coterminal angles differ by multiples of 2pi. -14pi/3 + 5(2pi) = 16pi/3, which lies in [4pi, 6pi).
Problem 2Difficulty: Mastery
Select the statement that explains why pi, not -pi, is the representative of -5pi in (-pi, pi].
AUse -pi because it is negative and closer to the original angle.
BUse pi because -pi is excluded from (-pi, pi] while pi is included.
CUse 0 because every odd multiple of pi is coterminal with 0.
DUse 2pi because it is the only positive coterminal angle.
Solution & Explanation:The angle -5pi is coterminal with both -pi and pi, but the interval (-pi, pi] excludes -pi and includes pi.
Problem 3Difficulty: Mastery
Which equation correctly adjusts -91pi/12 to a coterminal angle in (-pi, pi]?
A-91pi/12 + 3(2pi) = -19pi/12
B-91pi/12 + 4(2pi) = 5pi/12
C-91pi/12 + 5(2pi) = 29pi/12
D-91pi/12 - 4(2pi) = -187pi/12
Solution & Explanation:Adding 4 full rotations gives -91pi/12 + 96pi/12 = 5pi/12, and 5pi/12 lies in (-pi, pi].

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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: Determine an angle coterminal with a given angle that lies in a specified interval such as [0, 2π) or (-π, π]. 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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