Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.GT.4

TRIG.57 Inverse trigonometric functions and inverse graphs Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.57 Inverse trigonometric functions and inverse graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.57 Inverse trigonometric functions and inverse graphs - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.4. Skill statement in this prompt cell: Identify the correct restricted domain and range for an inverse trig function and select the correct inverse graph as a reflection across y = x. Associated standards listed with this skill in this prompt cell: UTRI.GT.4; CCSS HSF.TF.B.6; VA T.GT.2; FL MA.912.T.3.6. 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.57 Inverse trigonometric functions and inverse graphs skill assessments:

Problem 1Difficulty: Mastery

Which check is the strongest way to confirm that a candidate graph is the inverse of a restricted trig graph?

AEvery point (a, b) on the restricted graph has the matching point (b, a) on the candidate graph.

BThe candidate graph uses the same x-values as the restricted graph.

CThe candidate graph is periodic with the same period as the original graph.

DThe candidate graph has domain [0, pi] for every inverse trig function.

Solution & Explanation:Inverse graphs are reflections across y = x. That means corresponding points must have their coordinates swapped.

Problem 2Difficulty: Mastery

Which row correctly links the restricted cosine branch to its inverse function?

Aoriginal restriction [0, pi]; inverse arccos(x); inverse domain [-1, 1]; inverse range [0, pi]

Boriginal restriction [-pi/2, pi/2]; inverse arccos(x); inverse domain [-1, 1]; inverse range [-pi/2, pi/2]

Coriginal restriction [0, pi]; inverse arcsin(x); inverse domain [0, pi]; inverse range [-1, 1]

Doriginal restriction (-pi/2, pi/2); inverse arctan(x); inverse domain [-1, 1]; inverse range [0, pi]

Solution & Explanation:Cosine is restricted to [0, pi] for arccos. The inverse domain is the cosine output interval [-1, 1], and the inverse range is [0, pi].

Problem 3Difficulty: Mastery

The table for y = tan(x) restricted to (-pi/2, pi/2) includes (-pi/4, -1), (0, 0), and (pi/4, 1). Which table represents y = arctan(x)?

Ax: -1, 0, 1; y: -pi/4, 0, pi/4

Bx: -pi/4, 0, pi/4; y: -1, 0, 1

Cx: -1, 0, 1; y: pi/4, 0, -pi/4

Dx: -pi/2, 0, pi/2; y: -1, 0, 1

Solution & Explanation:The inverse table swaps inputs and outputs, so tangent outputs -1, 0, and 1 become arctan inputs.

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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.GT.4 (Primary standard selected for prompt fields in this prompt cell: UTRI.GT.4. Skill statement in this prompt cell: Identify the correct restricted domain and range for an inverse trig function and select the correct inverse graph as a reflection across y = x. Associated standards listed with this skill in this prompt cell: UTRI.GT.4; CCSS HSF.TF.B.6; VA T.GT.2; FL MA.912.T.3.6. Use this prompt-provided wording as the supporting standard description for this workflow.).