The Unit Circle

Today in class we learned about the unit circle and it's coordinates. One of the most important things we learned yesterday was using the Cos^2 + Sin^2 = 1

I'll do an example from the booklet

Example 3: The point P(theta) on the unit circle is not in quadrant 1. If Cos = 12/13, find the values of sin and tan.

1. Since your given sin you plug that in to the formula Cos^2 + Sin^2 = 1

(12/13)^2 + Sin^2 = 1

2. Move (12/13) to the other side

Sin^2 = 1-12/13

3. Square 12/13

Sin^2 = 1- 144/169

4. Find a common Denominator

Sin^2 = 169/169 - 144/169

5. Subtract the two values

25/169

6. Square root both sides to get sin by itself

Sin = +-5/13

7. Since Cos is positive in 4 Quadrants 4 and 1 you

Can only use 4 because it is stated that you cannot

use Quadrant 1

8. Therefore Sin -5/13

To find tan you divide 12/13 by 5/13 because tan = sin/cos

9. -5/13 x 13/12

10. tan = -5/12

Have a Nice Day!