1. Copyright © 2011 Pearson, Inc. 4.7 Inverse Trigonometric Functions

2. Copyright © 2011 Pearson, Inc. Slide 4.7 - 2 What you’ll learn about Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric and Inverse Trigonometric Functions Applications of Inverse Trigonometric Functions … and why Inverse trig functions can be used to solve trigonometric equations.

3. Copyright © 2011 Pearson, Inc. Slide 4.7 - 3 Inverse Sine Function             – 1  

4. Copyright © 2011 Pearson, Inc. Slide 4.7 - 4 Inverse Sine Function (Arcsine Function)

5. Copyright © 2011 Pearson, Inc. Slide 4.7 - 5 Example Evaluate sin –1 x Without a Calculator

6. Copyright © 2011 Pearson, Inc. Slide 4.7 - 6 Example Evaluate sin –1 x Without a Calculator

7. Copyright © 2011 Pearson, Inc. Slide 4.7 - 7 Example Evaluate sin -1 x Without a Calculator

8. Copyright © 2011 Pearson, Inc. Slide 4.7 - 8 Example Evaluate sin -1 x Without a Calculator

9. Copyright © 2011 Pearson, Inc. Slide 4.7 - 9 Inverse Cosine (Arccosine Function)    cos    cos –1  

10. Copyright © 2011 Pearson, Inc. Slide 4.7 - 10 Inverse Cosine (Arccosine Function)

11. Copyright © 2011 Pearson, Inc. Slide 4.7 - 11 Inverse Tangent Function (Arctangent Function)    ta     ta –1  

12. Copyright © 2011 Pearson, Inc. Slide 4.7 - 12 Inverse Tangent Function (Arctangent Function)

13. Copyright © 2011 Pearson, Inc. Slide 4.7 - 13 End Behavior of the Tangent Function The graphs of (a) y = tan x (restricted) and (b) y = tan –1 x. The vertical asymptotes of y = tan x are reflected to become the horizontal asymptotes of y = tan –1 x.

14. Copyright © 2011 Pearson, Inc. Slide 4.7 - 14 Composing Trigonometric and Inverse Trigonometric Functions

15. Copyright © 2011 Pearson, Inc. Slide 4.7 - 15 Example Composing Trig Functions with Arccosine

16. Copyright © 2011 Pearson, Inc. Slide 4.7 - 16 Example Composing Trig Functions with Arccosine  a triangle in which  = cos –1 x. The side opposite  (which is sin  ) is found by using the Pythagorean Theorem.

17. Copyright © 2011 Pearson, Inc. Slide 4.7 - 17 Example Composing Trig Functions with Arccosine

18. Copyright © 2011 Pearson, Inc. Slide 4.7 - 18 Quick Review

19. Copyright © 2011 Pearson, Inc. Slide 4.7 - 19 Quick Review Solutions