13.7 INVERSE TRIGONOMETRIC FUNCTIONSAlgebra II w/ trig

Principal Values of Sine, Cosine, and Tangent:

y = Sin x if and only if y = sin x and

y = Cos x if and only if y = cos x and

y = Tan x if and only if y = tan xand

2 2x

0 x

2 2x

Inverse Sine, Cosine, and Tangent:

Given y = Sin x, the inverse Sine Function is defined by or

Given y = Cos x, the inverse Cosine Function is defined by or

Given y= Tan x, the inverse Tangent Function is given by or

1y Sin x siny Arc x

1y Cos x cosy Arc x

1y Tan x tany Arc x

I. Write each equation in the form of an inverse function.(remember inverse is switching the x and y around)

A.

B.

C.

cos

1cos

2x

2 3sin

3 2

II. Solve each equation by finding the value of x to the nearest degree.

A. B.

C. D.

sin1Arc x 2cos

2x Arc

1 3

2Cos x tan( 3)x Arc

III. Find each value. Write angle measures in radians. Round to the nearest hundredth.

A. B.

C. D.

E.

1 3

2Cos

1 1tan2

Cos

cos[ tan( 1)]Arc 1 15sin 217

Cos

1 3cos 2

2Sin