1. 6.4 Inverses of the Trigonometric Functions Jan 5 Do Now Solve for x 1)Sin x = -1/2 2)Tan x = 1

2. Quiz Review Retakes by?

3. Inverse Trig Functions Recall: how to find inverse functions (switch x and y) Problem: If we switch x and y, the inverse fails the vertical line test (Draw picture here)

4. Inverse Trig Functions The 3 inverse trig functions (other 3 are reciprocals): 1) 2) 3)

5. Domain an Range To make these functions, we need to restrict the domain and range DomainRange [-1, 1]

6. Evaluating Inverse Trig Functions When evaluating these functions, we want to find the angle that results in the value. Note: because of the restriction in the ranges, we can only consider angles in each range

7. ex Find each of the following function values 1) 2) 3)

8. Calculators Calculators can be used to find inverse trig values Inverse sin,cos,tan – buttons Inverse reciprocals – your input will be the reciprocal

9. Ex Approximate using a calculator 1) 2) 3)

10. Closure Evaluate in radians and degrees HW: p.575 #1-35 odds

11. 6.4 Inverse Trig Functions Tues Jan 6 Do Now Evaluate in radians and degrees 1) 2)

12. HW Review: p.575 #1-35

13. Composition of Trig and Inverse Functions When evaluating a composition of trig and inverse trig values, compute the ‘inside’ first. Keep in mind the domain and range of each composition

14. Ex1 Simplify

15. Ex2 Simplify

16. Ex3 Simplify

17. Ex4 Simplify

18. Ex5 Simplify

19. Ex6 Simplify

20. Simplifying Compositions with X When simplifying a composition with a variable, draw a right triangle with an angle that has the given ratio

21. Ex Find

22. Ex Evaluate

23. Closure Evaluate HW: p.575 #37-67 odds