# 2.2: Round and Round She Goes

**At Grade**Created by: CK-12

*This activity is intended to supplement Trigonometry, Chapter 1, Lesson 7.*

## Problem 1 – Introduction to the Unit Circle

To the right, you will see a special circle known as the unit circle. It is centered at the origin and has a radius of one unit.

This circle is very important to the field of trigonometry. It is essential to develop an understanding of relationships between the angle theta,

*Note that the angle θ is measured from the positive x−axis.*

Right triangle trigonometry and knowledge of special right triangles can be applied to understanding the relationship between

1. Using the right triangle diagram, write an equation for

2. Using the right triangle diagram, write an equation for

Using the answers to Exercises 1 and 2, the unit circle can be relabeled as shown to the right. Note that the

3. What is the value of

4. What is the value of

5. Apply your knowledge of

6. Again, using your knowledge of

7. The cosine of

8. The sine of

9. The cosine of

10. The sine of

Check your results to Exercises 7–8 using your graphing calculator as shown to the right.

Note the **[ANGLE]**; and then press **ENTER**.

11. Using your knowledge of

12. The cosine of

13. The sine of

Check your results to Exercises 11–13 using your graphing calculator.

## Problem 2 – Extending the Pattern

Identify the coordinates of the following points in terms of

14.

15.

16.

Identify the measure of the following angles.

17.

18.

19.

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