Section 4.7 Inverse Trigonometric Functions Remember that an inverse function is a function that “undoes” the original function. A trig function maps an angle measure to a ratio. An inverse trig function maps a ratio back to an angle measure.

Compare sin x with sin-1 x. Notice that the domain is [-1,1]. Notice that the range is

Compare cos x with cos-1 x. Notice that the domain is [-1,1]. Notice that the range is

Compare tan x with tan-1 x. Notice that the domain is [-∞,∞]. Notice that the range is

Equivalent notations: sin-1 x  arcsin x cos-1 x  arccos x tan-1 x  arctan x By definition, answers to inverse trigonometric functions are always in radians.

Ex 1: Evaluate the following. a. arcsin b. sin-1 c. sin-1 2

Ex 2: Evaluate the following. a. arccos b. cos-1 -1 c. tan-1 0 d. arctan (-1)

Ex 3: Evaluate the following using a calculator. a. arctan (-8.45) b. cos-1 2 c. sin-1 (0.2447)

Suggested Assignment: Section 4.7 pg 316 – 317 #1 – 7, 13 – 24, 27 – 30