1. Warmup 9/2/15 Mr. C. believes he can prove that some kind of god must exist. The entire “natural” world around us works based on cause and effect. Thing B happens because thing A caused it. All of science relies on this. Nothing happens just “on its own”. If that’s so, where did the universe come from? Give this one some real thought. Understand the inverse trig functions pp 87: 3, 5, 7, 9 Objective Tonight’s Homework

2. Homework Help Let’s spend the first 10 minutes of class going over any problems with which you need help.

3. Notes on Inverse Trig Functions Our inverse trig functions are the functions that tell us what angle would give a desired result. For example, if we asked, ”The sine of what angle would equal 1?” What would our answer be?

4. Notes on Inverse Trig Functions Our inverse trig functions are the functions that tell us what angle would give a desired result. For example, if we asked, ”The sine of what angle would equal 1?” What would our answer be? π/2

5. Notes on Inverse Trig Functions Our inverse trig functions are the functions that tell us what angle would give a desired result. For example, if we asked, ”The sine of what angle would equal 1?” What would our answer be? π/2 but also 5 π/2, 9 π/2, 13 π/2, 17 π/2… hmmm.

6. Notes on Inverse Trig Functions We want to just have one answer, not infinite. To solve this, mathematicians have defined ranges for each inverse function.

7. Notes on Inverse Trig Functions We want to just have one answer, not infinite. To solve this, mathematicians have defined ranges for each inverse function. For sin(x), our range runs from -π/2 to π/2 For cos(x), our range runs from 0 to π For tan(x), our range runs from -∞ to ∞

8. Notes on Inverse Trig Functions Another thing to note… sin -1 (x) does not equal 1 / sin(x) or csc(x)! The inverse functions are totally unique things that must be dealt with as their own things!

9. Notes on Inverse Trig Functions Example: Solve sin 2 x = 1 (0<=x <2π)

10. Notes on Inverse Trig Functions Example: Solve sin 2 x = 1 (0<=x <2π) sin 2 x – 1 = 0

11. Notes on Inverse Trig Functions Example: Solve sin 2 x = 1 (0<=x <2π) sin 2 x – 1 = 0 (sin x – 1)(sin x + 1) = 0

12. Notes on Inverse Trig Functions Example: Solve sin 2 x = 1 (0<=x <2π) sin 2 x – 1 = 0 (sin x – 1)(sin x + 1) = 0 sin x = 1orsin x= –1

13. Notes on Inverse Trig Functions Example: Solve sin 2 x = 1 (0<=x <2π) sin 2 x – 1 = 0 (sin x – 1)(sin x + 1) = 0 sin x = 1orsin x= –1 x = π/2x = 3π/2

14. Group Practice Look at the example problems on pages 84 through 86. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help!

15. Exit Question Solve 2sin 2 (x) = 3 + 3cos(x) for (0 < x < 360) a) 60 b) 120 c) 120, 180 d) 120, 180, 240 e) 120, 180, 240, 360 f) None of the above