SECTION 4 6 INVERSE TRIGONOMETRIC FUNCTIONS Objectives Evaluate

SECTION 4. 6 INVERSE TRIGONOMETRIC FUNCTIONS Objectives: -Evaluate and Graph inverse trig functions -Find compositions of trig functions

Inverse Trig Functions �

Inverse SINE �

Inverse SINE �

Example 1: Find the exact value, it exists. �

Inverse COSINE � To make the cosine function one-to-one, the domain must be restricted to [0, ]. � The inverse cosine function is y = cos -1 x or arccosine function y = arccos x. The graph of y = cos -1 x is found by reflecting the graph of the restricted y = cosx in the line y = x. �

Inverse COSINE � � Recall that cos t is the x-coordinate of the point on the unit circle that corresponds to the angle or arc length, t. Because the range of y = cos -1 x is restricted to [0, ] , the possible angle measures of the inverse cosine function are located on the upper half of the unit circle

Example 2: Find the exact value, it exists. �

Inverse TANGENT �

Inverse TANGENT �

Example 3: Find the exact value, it exists. �

SUMMARY

Composition of Trig Functions �

SUMMARY of Composition Domain Restrictions

Example 6: Find the exact value, if it exists �

Example 7: Find the exact value �

Example 5: Application A) In a movie theater, a 32 -foot-tall screen is located 8 feet above ground. Write a function modeling the viewing angle θ for a person in theater whose eye-level when sitting is 6 feet above ground.

Example 5: B) In a movie theater, a 32 -foot-tall screen is located 8 feet above ground-level. Determine the distance that corresponds to the maximum viewing angle.