Circular Functions - Worksheet 7 - 12th Grade

Medium

Practice exact trigonometric values and identities with angle units and domains stated.

medium: Use other quadrants and basic identities.

24 problems · 20-25 minutes · Skills: trigonometry, circular functions, exact values

About This Worksheet

This medium-level worksheet contains 24 problems designed for 12th Grade students practicing circular functions & exact values. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Use radians, the unit circle and exact special-angle values.

  • Practice exact trigonometric values and identities with angle units and domains stated.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Find the exact value of sin(π/4 radians).
Solution Steps:
  1. Locate the angle on the unit circle.
  2. Cosine is the x-coordinate; sine is the y-coordinate.
  3. Use the quadrant to determine the sign.
Answer: √2/2
Tip: Check your result using the method in the example before moving to the next question.
1
Find the exact value of sin(π/4 radians).
2
Find the exact value of cos(3π/2 radians).
3
Find the exact value of sin(3π/4 radians).
4
Find the exact value of cos(0 radians).
5
Find the exact value of sin(π radians).
6
Find the exact value of cos(π/3 radians).
7
Find the exact value of sin(0 radians).
8
Find the exact value of cos(2π/3 radians).
9
Find the exact value of sin(π/2 radians).
10
Find the exact value of cos(3π/4 radians).
11
Find the exact value of sin(5π/6 radians).
12
Find the exact value of cos(5π/6 radians).
13
Find the exact value of sin(π/3 radians).
14
Find the exact value of cos(π/2 radians).
15
Find the exact value of sin(π/6 radians).
16
Find the exact value of cos(π/6 radians).
17
Find the exact value of sin(3π/2 radians).
18
Find the exact value of cos(π/4 radians).
19
Find the exact value of sin(2π/3 radians).
20
Find the exact value of cos(π radians).
21
Find the exact value of sin(2π/3 radians).
22
Find the exact value of cos(π/3 radians).
23
Find the exact value of sin(π radians).
24
Find the exact value of cos(π/6 radians).

Answer Key

1. √2/22. 03. √2/24. 15. 06. 1/27. 08. -1/29. 110. -√2/211. 1/212. -√3/213. √3/214. 015. 1/216. √3/217. -118. √2/219. √3/220. -121. √3/222. 1/223. 024. √3/2

Frequently Asked Questions

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What skills does this trigonometry & circular functions worksheet cover?

This worksheet focuses on trigonometry, circular functions, exact values. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 24 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.