1. Inverse
Trig Functions
Rita Korsunsky

2. To find the inverse of function y = sin x:
First: check if a function has an inverse function:
Use horizontal line test!
More than one point of intersection =>
Function does not pass horizontal line test =>
No inverse function, BUT…

3. Sin function is now one to one
(passes horizontal line test)!

4. To graph the inverse reflect function over line y = x.
Inverse sin function (Arcsinx or Sin-1x)
Domain and Range are switched

5. Graph of cos x and Arccosx
y = Arccos x
y = x
y = Arccosx
y =cos x

6. Arctan x tan x Arctanx Restrict the domain Reflect over y = x y = x

7. Graphs of Inverse Trig Functions

8. Example 1
Example 2

9. Example 3 Find the exact value of
If the value inside of arcsin, arccos or arctan is positive, the angle will always be in the I quadrant, so the answer will be:
The REFERENCE ANGLE

10. Example 4

11. Example 5

12. Example 6
Arctan (-1) = x. Find x

13. Example 7
Cos x = ?
positive 2 x 3

14. Example 8
Need to find sin of the angle where tan=

15. Example 9
Need to find tan of angle where sin=

16. Example 10

17. Graphing