SECTION 4 6 INVERSE TRIGONOMETRIC FUCTIONS Objectives Evaluate
SECTION 4. 6 INVERSE TRIGONOMETRIC FUCTIONS Objectives: -Evaluate and Graph inverse trig functions -Find compositions of trig functions
Inverse SINE �
Inverse SINE �
Inverse SINE �
Example 1: Find the exact value, if 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
Graphing Inverse Trig Functions � Rewrite the function in one of the following forms: � sin y=x � cos y = x � tan y = x � � Make a table of values, assigning radians from the restricted range to y. Plot the points and connect them with a smooth curve.
Example 4: Sketch the graph � y x
Example 4: Sketch the graph � y x
Example 4: Sketch the graph � y x
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) Determine the distance that corresponds to the maximum viewing angle.
Composition of Trig Functions �
SUMMARY of Composition Domain Restrictions
Example 6: Find the exact value, if it exists �
Example 7: Find the exact value �
Reciprocal Inverses �
Example 8: A) Write cot (arccos x) as an algebraic expression of x that does not involve trigonometric functions.
Example 8: B) Write cos(arctan x) as an algebraic expression of x that does not involve trigonometric functions.
Take A Picture For HW 1. 2. 3.
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