1. 6.5.3 – Other Properties of Inverse Functions

2. Just like other functions, we need to consider the domain and range of inverse trig functions To help us define the domain and range, let’s first consider the domain and range for the basic trig functions

3. Remember, the horizontal line test is used to determine if the inverse of a function is also a function Let’s start with the sine function to check the domain/range

4. Sin(x) What is the domain for sin(x)? What is the range for sin(x)?

5. Restricted Domain for sin -1 (x) = Restricted Range for sin -1 (x) =

6. Cos(x) What is the domain for cos(x)? What is the range for cos(x)?

7. Restricted Domain for cos -1 (x) = Restricted Range for cos -1 (x) =

8. Tan(x) What is the domain for tan(x)? What is the range for tan(x)?

9. Restricted Domain for tan -1 (x) = Restricted Range for tan -1 (x) =

10. Knowing our new domain and ranges, we now must make sure we choose the correct values when evaluating functions

11. Example. Evaluate the following expression, if possible. tan -1 (tan(7π/6))

12. Example. Evaluate the following expression, if possible. sin -1 (sin(2π/3))

13. Calculator Finally, we know our calculator may come in handy for many types of problems Whenever we use our calculators, always keep in mind the mode which they are in

14. Example. Find the measure of θ in degrees. Θ = cot -1 (0.57496998)

15. Example. Find the value of θ in radians. tan -1 (5.99999999)

16. Assignment Pg. 528 40-45 78-86 even