Inverse Trig FunctionsObj: Be able to evaluate inverse trig expressions.

TS: Explicitly assessing information and drawing conclusions.

Warm Up:Solve for x in the interval [0, π]

cos(x) = -½

Definition of Inverse Trigy = arcsin(x) if and only if sin(y) = xDomain: Range:

y = arccos(x) if and only if cos(y) = xDomain: Range:

y = arctan(x) if and only if tan(y) = xDomain: Range:

.

Definition of Inverse Trigy = csc-1(x) if and only if csc(y) = xDomain: Range:

y = sec-1 (x) if and only if sec(y) = xDomain: Range:

y = cot-1 (x) if and only if cot(y) = xDomain: Range:

.

Examples: Evaluate without calc

1cot 1

arctan 1

1 2sin

2

3arccos

2

1sin .5

1 3tan

3

1 2cos

2

1cos / 2 1csc 2

Examples: Approximate the values of each expression using your calculator.

arctan 2.75

1sin 0.91 arccos .2

1 1sin4

1tan 77 1 1cos

7