Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.GT.1

TRIG.54 Parent graphs of 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.54 Parent graphs of trigonometric functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.54 Parent graphs of trigonometric functions - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.1. Skill statement in this prompt cell: Select the correct parent graph for a given trigonometric function and identify key features such as intercepts, extrema, period, and asymptotes. Associated standards listed with this skill in this prompt cell: UTRI.GT.1; VA T.GT.1a-b; TEKS §111.42(c)(2)(F)-(J); FL MA.912.T.3.4. 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.54 Parent graphs of trigonometric functions skill assessments:

Problem 1Difficulty: Mastery

A graph has reciprocal range y<=-1 or y>=1, no y-intercept, and a vertical asymptote at x=0. Which parent graph is it, and why is it not secant?

Ay = csc(x), because cosecant is undefined at x=0 while secant has y-intercept 1

By = sec(x), because secant is undefined at x=0 while cosecant has y-intercept 1

Cy = cot(x), because cotangent has reciprocal range y<=-1 or y>=1

Dy = tan(x), because tangent has no y-intercept

Solution & Explanation:Cosecant is undefined at x=0 because sin(0)=0. Secant is defined at x=0 and equals 1.

Problem 2Difficulty: Mastery

A practice item asks for a parent graph with period 2*pi and no vertical asymptotes. The answer choices are sine, tangent, secant, and cotangent. Which choices can be eliminated immediately?

Atangent, secant, and cotangent

Bsine only

Csecant only

Dtangent and cotangent only

Solution & Explanation:Tangent and cotangent have period pi and vertical asymptotes, while secant has vertical asymptotes. Sine fits period 2*pi with no asymptotes.

Problem 3Difficulty: Mastery

Which complete feature set for y = csc(x) is accurate?

Adomain excludes x=k*pi; range y<=-1 or y>=1; period 2*pi; no x-intercepts

Bdomain excludes x=pi/2+k*pi; range all real; period pi; x-intercepts x=k*pi

Cdomain all real; range [-1,1]; period 2*pi; x-intercepts x=k*pi

Ddomain excludes x=pi/2+k*pi; range y<=-1 or y>=1; period pi; no x-intercepts

Solution & Explanation:Cosecant is reciprocal sine, so it is undefined at sine zeros, has reciprocal range, period 2*pi, and no x-intercepts.

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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.1 (Primary standard selected for prompt fields in this prompt cell: UTRI.GT.1. Skill statement in this prompt cell: Select the correct parent graph for a given trigonometric function and identify key features such as intercepts, extrema, period, and asymptotes. Associated standards listed with this skill in this prompt cell: UTRI.GT.1; VA T.GT.1a-b; TEKS §111.42(c)(2)(F)-(J); FL MA.912.T.3.4. Use this prompt-provided wording as the supporting standard description for this workflow.).