Inverse Functions

1. Inverse Functions How to find the angle.

2. So far… • Theta and a side has always been given to you. But what if we want to know the angle? 59 feet 37 feet θ

3. We know… 59 feet 37 feet θ

4. We know… You can’t divide by sin to get theta by itself. Sine is a function not a number or a variable. sin(θ) does not mean “sin times theta.” 59 feet 37 feet θ

5. Inverse functions In order to solve for theta we need to use inverse functions. The simple definition for an inverse function is “it undoes a function.”

6. Inverse functions You want θ? You have sin(θ)? Let’s undo that sin function!

7. Back to our problem… We want to find θ and we know 59 feet 37 feet θ

8. Back to our problem… 59 feet 37 feet θ

9. So… 59 feet 37 feet 38.84˚

10. Inverse Trig Functions The inverse of each trig function can be used by pressing the 2nd key followed by sin, cos, or tan.

11. Examples You’re driving to your favorite camp site with your family. You are forced to take a detour up a very steep dirt road. There’s a sign says the incline is 300 feet long, and you’ll be going up a total of 208 feet. Your car’s manual indicates it can only climb a maximum steepness of 30 ˚. Should your family attempt to go up this incline?

12. Examples You’re building some stairs from your lake house patio down to the beach. Your house is 19.5 feet above the beach, and you have only 12 feet between the patio and the water front. What is the smallest angle of ascension at which you can build your stairs?

13. Examples You’re robbing some fancy smancy apartment in a giant tower. Your escape plan involves zip-lining from the top of the tower to the roof of a near-by building with a helipad. You know the distance between the two buildings is 120 meters, and the helipad building is 30 meters shorter than fancy smancy building. If your angle of descent is greater than 65˚ you will zip too fast, bounce off the building, and you will die. What is the angle of your descent? Will your escape plan work?!