Section 6.1.2Inverse Sine and Cosine

Lesson Objective:

Students will:• Graph the relations for inverse sine

and cosine.• Restrict the range for to make them functions.• Use inverse functions to solve for

angles which are not special angles in the unit circle.

1 1sin and cosy x y x

Definition•The inverse of sin x is arcsin x or sin-

1x

•The inverse of cos x is arccos x or cos-1x

•The notation y=arcsin x can be thought of as “the arc whose sine is …” This connects the inverse back to the unit circle

Important IdeaTrig Function

Inverse Trig Function

siny x 1sin or arcsin x y x y

cosy x 1cos or x arccos x y y

ClosureAfter using the unit circle or calculator to find one angle for the inverse of a function, how can you easily find the additional angle?

AssignmentPg 276 #6-26 to 6-34