1. 5.2 Trigonometric Functions: Unit Circle Approach

2. The unit circle is a circle whose radius is 1 and whose center is at the origin. Since r = 1: becomes

3. (0, 1) (-1, 0) (0, -1) (1, 0) y x

4. (0, 1) (-1, 0) (0, -1) (1, 0) y x P = (a, b)

5. Let t be a real number and let P = (a, b) be the point on the unit circle that corresponds to t. The sine function associates with t the y-coordinate of P and is denoted by The cosine function associates with t the x-coordinate of P and is denoted by

6. If the tangent function is defined as Ifthe secant function is defined as the tangent function is defined asIf

7. the cotangent function is defined as

11. (0, 1) (-1, 0) (0, -1) (1, 0) y x P = (a, b)

12. If radians, the six trigonometric functions of the angle are defined as

13. y x r a b

14. Theorem

15. P=(a,b) (5, 0) Find the exact value of the remaining five trigonometric functions, given:

16. meaning

17. gives

18. P= (0,1) x y undefined

19. P= (1, 0) P= (a, b) x undefined

21. a =1