# 4.3: What’s the Difference?

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

*This activity is intended to supplement Trigonometry, Chapter 3, Lesson 5.*

## Problem 1 – Exploring the Angle Difference Formula for Cosine

Open the *Cabri Jr*. file called **UNITCIRC**. Observe a unit circle with points

Move points **ALPHA** key.

1. The

2. The

Use the file **UNITCIRC** to answer the following questions.

3. What is the sine of

4. What is the cosine of

5. What is the sine of

6. What is the cosine of

7. What is the sine of

8. What is the cosine of

9. Do you think the relationship between the values of sine and cosine for

## Problem 2 – Applying the Angle Difference Formula

The opening diagram for this activity is commonly used in the derivation of the angle difference formula for cosine.

This formula is useful in finding exact values for the cosine of angles other than those you may already know from the unit circle.

For each exercise below, use your graphing calculator first with and without the formula. Then use the **UNITCIRC** circle graph.

10. Find the value of

11. Find the value of

12. Find the value of

## Extension 1 – Derivation of the Angle Difference Formula for Cosine

The *Cabri Jr*. file that has been used for this activity will be used in the derivation of the angle difference formula for cosine. As you look at the sketches below, find the angle represented by

The angle difference formula for cosine will be derived using the diagrams below.

13. Apply the Law of Cosines to the figure to the right to find an equation representing

14. Apply the distance formula to the figure to the right to find an equation representing

15. Combine the two equations obtained in Exercises 13 and 14 by setting them equal to each other. Solve for **UNITCIRC**. Does your result agree with the directly calculated angle difference value? If not, check for algebraic and calculator entry errors.

## Extension 2 – Derivation of the Angle Sum Formula for Cosine

16. Now substitute

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
---|---|---|---|

Please Sign In to create your own Highlights / Notes | |||

Show More |

### Image Attributions

**Save or share your relevant files like activites, homework and worksheet.**

To add resources, you must be the owner of the section. Click Customize to make your own copy.