Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.3

TRIG.123 Resolve a vector into perpendicular components using trigonometry Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.123 Resolve a vector into perpendicular components using trigonometry. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.123 Resolve a vector into perpendicular components using trigonometry - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.3. Skill statement in this prompt cell: Select the correct horizontal and vertical components using sine and cosine for a given magnitude and direction. Associated standards listed with this skill in this prompt cell: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). 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.123 Resolve a vector into perpendicular components using trigonometry skill assessments:

Problem 1Difficulty: Mastery
A 64 km displacement is on a bearing of 310 degrees. Which formulas give the horizontal x and vertical y components?
Ax = 64 cos(310 deg); y = 64 sin(310 deg)
Bx = -64 sin(50 deg); y = -64 cos(50 deg)
Cx = 64 sin(50 deg); y = -64 cos(50 deg)
Dx = 64 sin(310 deg); y = 64 cos(310 deg)
Solution & Explanation:For bearings, x uses sine and y uses cosine because the angle is measured from north. At 310 degrees, x will be negative and y positive.
Problem 2Difficulty: Mastery
A planned diagram shows a 76-unit vector 33 degrees below the negative x-axis. Which formulas correctly resolve it?
Ax = -76 sin(33 deg); y = -76 cos(33 deg)
Bx = 76 cos(33 deg); y = -76 sin(33 deg)
Cx = -76 cos(33 deg); y = -76 sin(33 deg)
Dx = -76 cos(33 deg); y = 76 sin(33 deg)
Solution & Explanation:The reference angle is horizontal, so x uses cosine and y uses sine. Below the negative x-axis makes both components negative.
Problem 3Difficulty: Mastery
A 91-unit vector has standard-position angle 200 degrees. Which formulas correctly represent the components?
Ax = 91 sin(200 deg); y = 91 cos(200 deg)
Bx = 91 cos(200 deg); y = 91 sin(200 deg)
Cx = -91 cos(20 deg); y = 91 sin(20 deg)
Dx = 91 cos(20 deg); y = -91 sin(20 deg)
Solution & Explanation:A standard-position direction angle uses cosine for x and sine for y. The signs come from the trig values at 200 degrees.

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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.TA.3 (Primary standard selected for prompt fields in this prompt cell: UTRI.TA.3. Skill statement in this prompt cell: Select the correct horizontal and vertical components using sine and cosine for a given magnitude and direction. Associated standards listed with this skill in this prompt cell: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). Use this prompt-provided wording as the supporting standard description for this workflow.).

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