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The Unit Circle - Worksheet 7 - 11th Grade

Medium

Evaluate trig functions using the unit circle (Medium)

24 problems · 20-25 minutes · Skills: trigonometry, unit circle, radians

About This Worksheet

This medium-level worksheet contains 24 problems designed for 11th Grade students practicing the unit circle. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

The unit circle is the master reference for all of trigonometry. Memorizing it enables rapid evaluation of trig functions at standard angles — a skill required throughout calculus, physics, and engineering. More importantly, the unit circle reveals that trig functions are fundamentally about the coordinates of points on a circle, connecting geometry and algebra in a profound way.

  • Understand radian measure and convert between degrees and radians
  • Identify the coordinates of standard angles on the unit circle in all four quadrants
  • Evaluate the six trig functions at standard angles using unit circle coordinates without a calculator
  • Find all angles with a given trig value using reference angles and quadrant signs
  • Use the unit circle to explain why sine is odd and cosine is even

How to Solve: Worked Example

Example Problem: Find cos(135°).
Solution Steps:
  1. 135° is in Quadrant II (between 90° and 180°).
  2. The reference angle is 180° − 135° = 45°.
  3. cos(45°) = √2/2.
  4. In Quadrant II, cosine is negative.
  5. cos(135°) = −√2/2.
Answer: cos(135°) = −√2/2
Tip: Use reference angles: find the equivalent acute angle, then apply the sign rule for the quadrant (ASTC).
1
6 + 5 =
2
2 + 10 =
3
9 + 2 =
4
6 + 2 =
5
4 + 6 =
6
4 + 5 =
7
2 + 7 =
8
7 + 7 =
9
7 + 7 =
10
10 + 2 =
11
3 + 5 =
12
8 + 5 =
13
3 + 3 =
14
9 + 10 =
15
1 + 8 =
16
1 + 3 =
17
6 + 8 =
18
4 + 7 =
19
3 + 6 =
20
4 + 2 =
21
9 + 7 =
22
5 + 6 =
23
5 + 2 =
24
10 + 3 =

Answer Key

1. 112. 123. 114. 85. 106. 97. 98. 149. 1410. 1211. 812. 1313. 614. 1915. 916. 417. 1418. 1119. 920. 621. 1622. 1123. 724. 13

Frequently Asked Questions

How do I download this the unit circle - worksheet 7 worksheet?

Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this trigonometry worksheet cover?

This worksheet focuses on trigonometry, unit circle, radians. It is designed for 11th 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.