Inverse Trigonometric Functions

Example problem 2: tan(cos-1(-.6))

-.6 = -6/10 = cos = adj/hyp. therefore in the unit circle you have a 6-8-10 triangle of which the tangent is 8/-6.

What are they?

Behave a lot like regular inverses in that sin-1(sinx) = x, must pass horizontal line test, etc In order to pass the horizontal line test with periodic functions you have to restrict them down to the function's principal part, aka one single period

cos-1(x)

cos(theta) = x 0 <= theta <= Pi -1<= y <=1 Can be in first or second quadrant

sin-1(x)

sin(theta) = x -Pi/2 <= theta <= Pi/2 -1<= y <=1 Can be in first or fourth quadrant

Example problem 1: sin-1(1/2)

sin(theta) is 1/2, so reference angle must be 30 degrees. Since it's a sin graph, can be in first or fourth quadrant, but the 1/2 is positive, so it must be first quadrant: 30 degrees.

tan-1(x)

tan(theta) = x -Pi/2 <= theta <= Pi/2 All real y values Can be in first or fourth quadrant

Sinx

the principal part of sinx. (same goes for cos, tan, etc)