Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-TF.1-9(+)

Pre CAL.80 Graphs of Tangent and Reciprocal Trigonometric Functions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.80 Graphs of Tangent and Reciprocal Trigonometric Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.80 Graphs of Tangent and Reciprocal Trigonometric Functions - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement: Given a tangent or reciprocal trigonometric function, identify asymptotes, period, and key transformations and select the correct graph. Associated standards listed with this skill: CCSS HSF-TF.1-9(+); CCSS HSF-IF.7e; CCSS HSG-SRT.C.6-8; SMP 1,2,3,5,7,8; AP Precalculus CED Unit 3; TX §111.42(c)(4)(A-D), (c)(5)(I); FL MA.912.T.1.3-1.8, MA.912.T.2.1-2.5, MA.912.T.3.1-3.3, MA.912.T.4.1-4.7; VA T.CT.1-2, T.GT.1-2, T.IE.1-3.

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

Pre-Calculus

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 Pre CAL.80 Graphs of Tangent and Reciprocal Trigonometric Functions skill assessments:

Problem 1Difficulty: Mastery

Which graph description matches y = -2sec(3(x + pi/9)) + 1?

ASecant branches with period 2pi/3, asymptotes x = pi/18 + k*pi/3, range y <= -1 or y >= 3, vertices at (-pi/9, -1) and (2pi/9, 3)

BSecant branches with period pi/3, asymptotes x = -pi/9 + k*pi/3, range y <= -1 or y >= 3

CCosecant branches with period 2pi/3, asymptotes x = -pi/9 + k*pi/3, range y <= -1 or y >= 3

DSecant branches with period 2pi/3, asymptotes x = pi/18 + k*2pi/3, range y <= -3 or y >= 1

Solution & Explanation:The shift is h = -pi/9 and b = 3, so period is 2pi/3. Secant asymptotes are h + pi/(2b) + k*pi/b = pi/18 + k*pi/3. The range uses k = 1 and |a| = 2.

Problem 2Difficulty: Mastery

Which complete graphing plan matches y = (1/2)csc((pi/4)(x + 1)) + 3?

Aperiod 8, asymptotes x = -1 + 4k, range y <= 2.5 or y >= 3.5, first positive vertex at (1, 3.5)

Bperiod 4, asymptotes x = -1 + 8k, range y <= 2.5 or y >= 3.5, first positive vertex at (1, 3.5)

Cperiod 8, asymptotes x = 1 + 4k, range y <= -3.5 or y >= -2.5, first positive vertex at (-1, 3.5)

Dperiod 8, asymptotes x = -1 + 4k, range all real numbers, first positive vertex at (1, 3.5)

Solution & Explanation:The b-value pi/4 gives period 8. Cosecant asymptotes satisfy (pi/4)(x + 1) = k*pi, so x = -1 + 4k. The range is 3 +/- 0.5 outside the gap, and the first positive vertex is 2 units after x = -1.

Problem 3Difficulty: Mastery

Which features match y = -5cot((pi/2)(x - 3)) - 2?

Aperiod 2, asymptotes x = 3 + 2k, increasing branches, range all real numbers

Bperiod 4, asymptotes x = 3 + 2k, decreasing branches, range all real numbers

Cperiod 2, asymptotes x = 3 + k, increasing branches, range y <= -7 or y >= 3

Dperiod pi/2, asymptotes x = 3 + 2k, increasing branches, range all real numbers

Solution & Explanation:Cotangent period is pi/(pi/2) = 2, so asymptotes are x = 3 + 2k. The negative coefficient makes branches increase, and cotangent range remains all real numbers.

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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 Pre-Calculus Math students. It aligns with educational standard HSF-TF.1-9(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement: Given a tangent or reciprocal trigonometric function, identify asymptotes, period, and key transformations and select the correct graph. Associated standards listed with this skill: CCSS HSF-TF.1-9(+); CCSS HSF-IF.7e; CCSS HSG-SRT.C.6-8; SMP 1,2,3,5,7,8; AP Precalculus CED Unit 3; TX §111.42(c)(4)(A-D), (c)(5)(I); FL MA.912.T.1.3-1.8, MA.912.T.2.1-2.5, MA.912.T.3.1-3.3, MA.912.T.4.1-4.7; VA T.CT.1-2, T.GT.1-2, T.IE.1-3.).