An Inverse Function What was that again? 6-5 Inverse Trig An Inverse Function What was that again?

Get out those Calculators Please find the following: sin-10 6. cos-10 sin-1.5 7. cos-1.5 sin-11 8. cos-11 sin-1(-.5) 9. cos-1(-.5) sin-1(-1) 10. cos-1(-1)

What is an inverse function? What is the notation? Arc = “-1” In a way, you have been practicing the inverse trig process. In section 7-6, you had the trig value and found the angle.

f(x) = sin x its inverse would be What is the problem here? The inverse ISN’T a function!!

How do we take care of that? Lets look at the graphs: Therefore, there are limits on the answers that you can get. Use your calculator to find cos-1(-.5) What did you see?

Each function has a limited Range For sin-1x, csc-1x, tan-1x QI or QIV (go clockwise!) For cos-1x, sec-1x, cot-1x QI or QII

REMEMBER With inverse trig you give only ONE answer!! The answer must be the closest answer to 0. An answer in quadrant 4 such as 300 must be given as -60. BE Careful!!

A Hint To give yourself something to remember, use the phrase “What angle has a” for the symbol -1. SO, lets try some problems.