1. Use your knowledge of UC to find the values of 

2. Section 7-6 The Inverse Trigonometric Functions Objective: To find values of the inverse trigonometric functions.

3. Reminder about reference angles

5. REVIEW CONCEPTS:

6. review  One to one function  Restricted domain  Inverse functions –Inverse function equations algebraically. –Inverse functions graphically.

7. Trig FUNCTIONS  Sine, cosine and tangent are all functions.  Are they all one-to-one functions?

8. Notice how the axes are scaled!

9. Trig functions Does tan θ have an inverse that is a function? Justify your answer. If you answered no, you are right. However, we need to have a way to “undo” tan θ.

10. The graph does not have an inverse function.

11. Inverse of trig functions Restrict domain to f(x)=Tan x Inverse function is Tan -1 x Notice T is capitalized

12. Tan x has an inverse. Notice how the axes are scaled!

15. Sec 7.6 Warm Up Day 2

16. Notice how the axes are scaled!

17. Inverse of trig functions

18. Notice how the axes are scaled!

21. Inverse of trig functions Restrict domain to 0 <x <  F(x)=Cos x Inverse function is Cos -1 x

22. Notice how the axes are scaled!

26. graphs of trig functions graph of inverse funtions

27. Restricted domains summarized: Notice the restricted domain for each of the inverse functions includes the first quadrant… i.e. the reference angle.

28. Sine Function: sin(30°) = 0.5 Inverse Sine: Sin -1 (0.5) = 30°

29.  tan(angle value)= ratio  Tan -1 (ratio)= angle value  sin(angle value)= ratio  Sin -1 (ratio)= angle value  cos(angle value)= ratio  Cos -1 (ratio)= angle value

30. Example 1  Find Tan -1 2 with a calculator. 0<θ<360°  First make sure your calculator is in the correct mode.

31. Example 2  Find Tan -1 (-1) without a calculator. 0<θ<2 

32. Restricted domains summarized:

33. Use your knowledge UC and RA:

34. Warm UP Day 2: :

35. Parent graph: sine function

36. review graphing:  Study the graphs below. Draw inverse of each graph.

38. Example 3  A.) Find Sin -1 (-0.8) with a calculator. 0<θ<360°  B.) Find Cos -1 (-0.5) without a calculator. 0<θ<2 

39. Example 4 Hint: pay attention to restricted domain. A) Find the value of the above expression without a calculator.

40. Example 4 Hint: pay attention to restricted domain. B) Find the value of with a calculator.

41. No matter the mode setting is…

42. Homework  Sec 7.6 written exercises  Day 1: #1-9 All, read #10  Day 2: #11-21 All

43. Review http://hotmath.com/help/gt/miniprecalcgt/se ction_5_1.html