Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.UC.2

TRIG.45 Find trig values for angles outside the first quadrant Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.45 Find trig values for angles outside the first quadrant. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.45 Find trig values for angles outside the first quadrant - Primary standard selected for prompt fields in this prompt cell: UTRI.UC.2. Skill statement in this prompt cell: Select the equivalent reference-angle expression (using periodicity or symmetry) and determine the correct trig value. Associated standards listed with this skill in this prompt cell: UTRI.UC.2; CCSS HSF.TF.A.3 (+); FL MA.912.T.2.1; VA T.CT.2c; UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. 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.45 Find trig values for angles outside the first quadrant skill assessments:

Problem 1Difficulty: Mastery

The angle is measured in radians. Select the option that reduces -69pi/4 correctly before evaluating cos(-69pi/4).

Acos(-69pi/4 + 18pi) = cos(pi - pi/4) = sqrt(2)/2

Bcos(-69pi/4 + 18pi) = cos(pi + pi/4) = sqrt(2)/2

Ccos(-69pi/4 + 18pi) = cos(2pi - pi/4) = sqrt(2)/2

Dcos(-69pi/4 + 18pi) = cos(pi - pi/4) = -sqrt(2)/2

Solution & Explanation:-69pi/4 is coterminal with 3pi/4 after adding full rotations. 3pi/4 is in Quadrant II with reference angle pi/4. cosine is negative in Quadrant II, so cos(-69pi/4) = cos(pi - pi/4) = -sqrt(2)/2.

Problem 2Difficulty: Mastery

The angle is measured in radians. Reduce 67pi/4 to a coterminal angle, then evaluate sin(67pi/4). Which statement is correct?

Asin(16pi + (pi - pi/4)) = -sqrt(2)/2

Bsin(16pi + (pi + pi/4)) = -sqrt(2)/2

Csin(16pi + (pi - pi/4)) = sqrt(2)/2

Dsin(16pi + (2pi - pi/4)) = -sqrt(2)/2

Solution & Explanation:67pi/4 is coterminal with 3pi/4 after subtracting full rotations. 3pi/4 is in Quadrant II with reference angle pi/4. sine is positive in Quadrant II, so sin(67pi/4) = sin(16pi + (pi - pi/4)) = sqrt(2)/2.

Problem 3Difficulty: Mastery

Use a coterminal positive angle to evaluate cot(-2580 deg). Which option is correct?

Acot(-2580 deg + 2880 deg) = cot(360 deg - 60 deg) = sqrt(3)/3

Bcot(-2580 deg + 2880 deg) = cot(360 deg - 60 deg) = -sqrt(3)/3

Ccot(-2580 deg + 2880 deg) = cot(180 deg - 60 deg) = sqrt(3)/3

Dcot(-2580 deg + 2880 deg) = cot(180 deg + 60 deg) = sqrt(3)/3

Solution & Explanation:-2580 deg is coterminal with 300 deg after adding full rotations. 300 deg is in Quadrant IV with reference angle 60 deg. cotangent follows tangent is negative in Quadrant IV, so cot(-2580 deg) = cot(360 deg - 60 deg) = -sqrt(3)/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.UC.2 (Primary standard selected for prompt fields in this prompt cell: UTRI.UC.2. Skill statement in this prompt cell: Select the equivalent reference-angle expression (using periodicity or symmetry) and determine the correct trig value. Associated standards listed with this skill in this prompt cell: UTRI.UC.2; CCSS HSF.TF.A.3 (+); FL MA.912.T.2.1; VA T.CT.2c; UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.).