Inverse Trigonometric Functions Section 4.7 Inverse Trigonometric Functions

Objective By following instructions students will be able to: Evaluate inverse sine functions. Evaluate other inverse trigonometric functions. Evaluate compositions of trigonometric functions.

Inverse Sine Function y= arc sin x Recall: in order for a function to have an inverse, it must pass the horizontal line test. iff where: 1. 2. 3. Domain: [-1,1] 4. Range:

Example 1: Evaluating the Inverse Sine Function If possible, find the exact value. a) b) c)

Example 2: Graphing the Arcsine Function Sketch the graph of

Inverse Cosine Function Y= arc cos x Recall: in order for a function to have an inverse, it must pass the horizontal line test. iff where: 1. 2. 3. Domain: [-1,1] 4. Range:

Inverse Tangent Function Y= arc tan x Recall: in order for a function to have an inverse, it must pass the horizontal line test. iff where: 1. 2. 3. Domain: 4. Range:

Example 3: Evaluating Inverse Trigonometric Functions Find the exact value. a) b) c) d)

Example 4: Calculators and Inverse Trigonometric Functions If possible, use a calculator to approximate the value. a) b) c)

Compositions of Functions Inverse Properties If… Then… and

Example 5: Use Inverse Properties If possible, find the exact value. a) b) c)

Example 6: Evaluating Composition of Functions Find the exact value of… a) b)

Example 7: Some Problems from Calculus Write each of the following as an algebraic expression in x. a) b)

Revisit Objective Did we… Evaluate inverse sine functions? Evaluate other inverse trigonometric functions? Evaluate compositions of trigonometric functions?

Homework Pg 351 # 1-53 ALL