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TRIG.47 Determine all six trig functions from one function value and 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.47 Determine all six trig functions from one function value and quadrant. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.47 Determine all six trig functions from one function value and quadrant - Determine all six trig functions from one function value and quadrant

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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.47 Determine all six trig functions from one function value and quadrant skill assessments:

Problem 1Difficulty: Mastery

Angle θ lies in Quadrant IV. If csc(θ) = -√10 over 2, select the complete set of sin, cos, tan, csc, sec, and cot.

Asin(θ) = -√10 over 5, cos(θ) = -√15 over 5, tan(θ) = √6 over 3, csc(θ) = -√10 over 2, sec(θ) = -√15 over 3, cot(θ) = √6 over 2

Bsin(θ) = √10 over 5, cos(θ) = √15 over 5, tan(θ) = √6 over 3, csc(θ) = √10 over 2, sec(θ) = √15 over 3, cot(θ) = √6 over 2

Csin(θ) = √10 over 5, cos(θ) = -√15 over 5, tan(θ) = -√6 over 3, csc(θ) = √10 over 2, sec(θ) = -√15 over 3, cot(θ) = -√6 over 2

Dsin(θ) = -√10 over 5, cos(θ) = √15 over 5, tan(θ) = -√6 over 3, csc(θ) = -√10 over 2, sec(θ) = √15 over 3, cot(θ) = -√6 over 2

Solution & Explanation:Use the quadrant to get the signs (Quadrant IV). First invert to get sin(θ) = -√10 over 5. Then use sin(θ) squared + cos(θ) squared = 1 to find the missing sin or cos. Here, sin(θ) = -√10 over 5 and cos(θ) = √15 over 5. Compute tan(θ) = sin(θ) over cos(θ) = -√6 over 3, and take reciprocals for csc, sec, cot: csc(θ) = -√10 over 2, sec(θ) = √15 over 3, cot(θ) = -√6 over 2.

Problem 2Difficulty: Mastery

Angle θ lies in Quadrant III. If sec(θ) = -√101 over 10, select the complete set of sin, cos, tan, csc, sec, and cot.

Asin(θ) = √101 over 101, cos(θ) = -10√101 over 101, tan(θ) = -1 over 10, csc(θ) = √101, sec(θ) = -√101 over 10, cot(θ) = -10

Bsin(θ) = -√101 over 101, cos(θ) = 10√101 over 101, tan(θ) = -1 over 10, csc(θ) = -√101, sec(θ) = √101 over 10, cot(θ) = -10

Csin(θ) = -√101 over 101, cos(θ) = -10√101 over 101, tan(θ) = 1 over 10, csc(θ) = -√101, sec(θ) = -√101 over 10, cot(θ) = 10

Dsin(θ) = √101 over 101, cos(θ) = 10√101 over 101, tan(θ) = 1 over 10, csc(θ) = √101, sec(θ) = √101 over 10, cot(θ) = 10

Solution & Explanation:Use the quadrant to get the signs (Quadrant III). First invert to get cos(θ) = -10√101 over 101. Then use sin(θ) squared + cos(θ) squared = 1 to find the missing sin or cos. Here, sin(θ) = -√101 over 101 and cos(θ) = -10√101 over 101. Compute tan(θ) = sin(θ) over cos(θ) = 1 over 10, and take reciprocals for csc, sec, cot: csc(θ) = -√101, sec(θ) = -√101 over 10, cot(θ) = 10.

Problem 3Difficulty: Mastery

Given cot(θ) = 9 over 2 and θ is in Quadrant I, which option lists all six trig values?

Asin(θ) = -2√85 over 85, cos(θ) = -9√85 over 85, tan(θ) = 2 over 9, csc(θ) = -√85 over 2, sec(θ) = -√85 over 9, cot(θ) = 9 over 2

Bsin(θ) = 2√85 over 85, cos(θ) = 9√85 over 85, tan(θ) = 2 over 9, csc(θ) = √85 over 2, sec(θ) = √85 over 9, cot(θ) = 9 over 2

Csin(θ) = 2√85 over 85, cos(θ) = -9√85 over 85, tan(θ) = -2 over 9, csc(θ) = √85 over 2, sec(θ) = -√85 over 9, cot(θ) = -9 over 2

Dsin(θ) = -2√85 over 85, cos(θ) = 9√85 over 85, tan(θ) = -2 over 9, csc(θ) = -√85 over 2, sec(θ) = √85 over 9, cot(θ) = -9 over 2

Solution & Explanation:Quadrant I tells you the signs of sin and cos. First invert to get tan(θ) = 2 over 9. Treat tan(θ) as opposite over adjacent, then find the hypotenuse with the Pythagorean Theorem. This gives sin(θ) = 2√85 over 85 and cos(θ) = 9√85 over 85. Then tan(θ) = 2 over 9, and the reciprocals are csc(θ) = √85 over 2, sec(θ) = √85 over 9, cot(θ) = 9 over 2.

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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 TRIG.47 (Determine all six trig functions from one function value and quadrant).