Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.GT.1

TRIG.53 Connect the unit circle to sine and cosine 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.53 Connect the unit circle to sine and cosine graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.53 Connect the unit circle to sine and cosine graphs - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.1. Skill statement in this prompt cell: Select the graph feature or plotted point that corresponds to a given unit-circle position and vice versa. 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; UTRI.UC.1; CCSS HSF.TF.A.2; FL MA.912.T.2.1-2.2; VA T.CT.2b; NY AII-F.TF.1-2. 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.53 Connect the unit circle to sine and cosine graphs skill assessments:

Problem 1Difficulty: Mastery
At one angle in Quadrant IV, the cosine graph point is (theta, 1/2) and the sine graph point is (theta, -sqrt(3)/2). Which angle and unit-circle point match?
Atheta = pi/3 with point (1/2, sqrt(3)/2)
Btheta = 4pi/3 with point (-1/2, -sqrt(3)/2)
Ctheta = 7pi/6 with point (-sqrt(3)/2, -1/2)
Dtheta = 5pi/3 with point (1/2, -sqrt(3)/2)
Solution & Explanation:Cosine gives x = 1/2 and sine gives y = -sqrt(3)/2. In Quadrant IV, that point is (1/2, -sqrt(3)/2) at theta = 5pi/3.
Problem 2Difficulty: Mastery
Which connection is correct for theta = 9pi/4?
AIt shares the unit-circle point of pi/4, so the graph point must be plotted at horizontal position pi/4 only.
BIt shares the unit-circle point of 3pi/4, so sine is sqrt(2)/2 and cosine is -sqrt(2)/2.
CIt shares the unit-circle point of pi/4, so sine and cosine graph values are both sqrt(2)/2 at horizontal position 9pi/4.
DIt is outside one rotation, so it has no sine or cosine graph value.
Solution & Explanation:Since 9pi/4 = 2pi + pi/4, it is coterminal with pi/4. The graph uses the actual input 9pi/4 as the horizontal coordinate, and both values are sqrt(2)/2.
Problem 3Difficulty: Mastery
A point on y = sin(theta) is (theta, sqrt(3)/2), and the point on y = cos(theta) at the same theta is (theta, -1/2). Which theta in 0 <= theta <= 2pi fits?
Api/3
B2pi/3
C4pi/3
D5pi/3
Solution & Explanation:The values make the unit-circle point (cos, sin) = (-1/2, sqrt(3)/2), which is theta = 2pi/3.

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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 graph feature or plotted point that corresponds to a given unit-circle position and vice versa. 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; UTRI.UC.1; CCSS HSF.TF.A.2; FL MA.912.T.2.1-2.2; VA T.CT.2b; NY AII-F.TF.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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