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

Pre CAL.79 Graphs of Sine and Cosine 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.79 Graphs of Sine and Cosine Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.79 Graphs of Sine and Cosine Functions - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement in this prompt cell: Given a sine or cosine equation or graph, determine amplitude, period, midline, and shifts and select the matching graph or equation. Associated standards listed with this skill in this prompt cell: 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. 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

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.79 Graphs of Sine and Cosine Functions skill assessments:

Problem 1Difficulty: Mastery
A student uses the y-intercept of y = 6 cos(2x) + 1 and says the midline is y = 7. What is the correct midline?
Ay = 1
By = 6
Cy = 7
Dy = -5
Solution & Explanation:The y-intercept is 6 cos(0) + 1 = 7, which is a maximum. The midline is the vertical shift, y = 1.
Problem 2Difficulty: Mastery
Use the half-speed sine graph shown. Which set of features describes the curve?
AAmplitude 4, period 4pi, midline y = 1, shift right 2pi/3
BAmplitude 4, period 2pi, midline y = 1, shift right pi/3
CAmplitude 1, period 4pi, midline y = 4, shift right 2pi/3
DAmplitude 4, period 4pi, midline y = -1, shift left 2pi/3
Solution & Explanation:The graph is y = 4 sin(x/2 - pi/3) + 1. Since x/2 - pi/3 = (1/2)(x - 2pi/3), the shift is right 2pi/3 and the period is 4pi.
Problem 3Difficulty: Mastery
Which equation represents y = 3 cos(2x) - 4 shifted right pi/6?
Ay = 3 cos(2(x - pi/6)) - 4
By = 3 cos(2(x + pi/6)) - 4
Cy = 3 cos(2x - pi/6) - 4
Dy = 3 cos(2x) - 4 - pi/6
Solution & Explanation:To shift the whole graph right pi/6, replace x with x - pi/6 inside the original function: y = 3 cos(2(x - pi/6)) - 4.

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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 in this prompt cell: Given a sine or cosine equation or graph, determine amplitude, period, midline, and shifts and select the matching graph or equation. Associated standards listed with this skill in this prompt cell: 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. Use this prompt-provided wording as the supporting standard description for this workflow.).

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