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

Pre CAL.76 Unit Circle Definitions of Sine and Cosine 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.76 Unit Circle Definitions of Sine and Cosine. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.76 Unit Circle Definitions of Sine and Cosine - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement in this prompt cell: Given an angle on the unit circle, determine the coordinates and select the correct values of sine and cosine. 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.76 Unit Circle Definitions of Sine and Cosine skill assessments:

Problem 1Difficulty: Mastery

For theta = 3pi - pi/4, which values of sin(theta) and cos(theta) are correct?

Asin(theta) = -sqrt(3)/2; cos(theta) = -1/2

Bsin(theta) = sqrt(2)/2; cos(theta) = -sqrt(2)/2

Csin(theta) = -sqrt(2)/2; cos(theta) = sqrt(2)/2

Dsin(theta) = -sqrt(2)/2; cos(theta) = -sqrt(2)/2

Solution & Explanation:Use the definition point = (cos theta, sin theta). Simplify to 11pi/4, then subtract 2pi to get 3pi/4. At 135 degrees (3pi/4), the x-coordinate is -sqrt(2)/2 and the y-coordinate is sqrt(2)/2; therefore cos(theta) = -sqrt(2)/2 and sin(theta) = sqrt(2)/2.

Problem 2Difficulty: Mastery

A rotation goes clockwise 300 degrees from the positive x-axis. Which statement gives the resulting point and trig values?

Acos(theta) = sqrt(2)/2, sin(theta) = sqrt(2)/2, and the terminal point is (sqrt(2)/2, sqrt(2)/2)

Bcos(theta) = -sqrt(2)/2, sin(theta) = sqrt(2)/2, and the terminal point is (-sqrt(2)/2, sqrt(2)/2)

Ccos(theta) = -sqrt(2)/2, sin(theta) = -sqrt(2)/2, and the terminal point is (-sqrt(2)/2, -sqrt(2)/2)

Dcos(theta) = 1/2, sin(theta) = sqrt(3)/2, and the terminal point is (1/2, sqrt(3)/2)

Solution & Explanation:On the unit circle, the terminal point is (cos theta, sin theta). Clockwise 300 degrees is -300 degrees, which is coterminal with 60 degrees. For 60 degrees (pi/3), the point is (1/2, sqrt(3)/2), so cos(theta) = 1/2 and sin(theta) = sqrt(3)/2.

Problem 3Difficulty: Mastery

A rotation makes two full counterclockwise turns and then 150 degrees more. Which point and sine/cosine values result?

Apoint = (-sqrt(3)/2, 1/2); sin(theta) = 1/2; cos(theta) = -sqrt(3)/2

Bpoint = (-1, 0); sin(theta) = 0; cos(theta) = -1

Cpoint = (0, -1); sin(theta) = -1; cos(theta) = 0

Dpoint = (1/2, -sqrt(3)/2); sin(theta) = -sqrt(3)/2; cos(theta) = 1/2

Solution & Explanation:On the unit circle, the terminal point is (cos theta, sin theta). Two full turns do not change the terminal point, so the angle is coterminal with 150 degrees. For 150 degrees (5pi/6), the point is (-sqrt(3)/2, 1/2), so cos(theta) = -sqrt(3)/2 and sin(theta) = 1/2.

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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 an angle on the unit circle, determine the coordinates and select the correct values of sine and cosine. 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.).