Warm-up – 9/18/2015Do your warm-up in your notes1) 2)3)

Agenda• Warm-up• 4.7 notes (day 3)- • Finding values of inverse

functions (domain/range)• Compositions of inverses

Assignment 4.7cPg. 547 32-72 Every other even, 95, 100, 108

Assignment #3A Solutions2) 4) 6)

8) 10) 12)

14) 16) 18)

20) 22) 24)

26) 28) 30)

03

3

4

6

5

30.1

11.168.049.0

6

4

4

0

56.154.1

What you need to know and be able to do…• Understand the graphs, domain and range of

the inverse sine, cosine and tangent.• Use the inverse functions to find the exact

angle measure given a value of sine, cosine and tangent.

• Be able to find the composition of functions with their inverses and composite expressions.

(4.7) Inverse Trigonometric Functions

11

Graphs of Inverse Trigonometric Functions

The basic idea of the inverse function is the same whether it is arcsin, arccos, or arctan

Finding the exact value of inverse trig functions

Notation:You’ll see inverse trig functions use two equivalent notations:

They both mean the same thing. The notation used in our text is . Other texts may use the other notation and Khan Academy or other video help may use

In addition, we are not studying inverse cot, inverse sec or inverse csc functions.

1sin arcsinx x 1cos arccosx x 1tan arctanx x

1sin x

arcsin x

Examples: Finding the exact valueFind the exact value of the expression.A)

B)

C)

1 1sin

2

1 2cos

2

1tan 3

Examples: Using your calculatorUse your calculator to find the value of the expression rounded to two decimal places.A)

B)

1sin 0.3

1 5cos

7

• For all functions and their inverses

and

When x in the domain of f.

Inverse properties From p. 543 (do not copy for notes):

Evaluating Compositions of Functions and their inverses

xxff 1 xxff 1

The Sine Function and Its Inversesin(sin-1 x) = x for every x in the interval [-1, 1].sin-1(sin x) = x for every x in the interval [-/2,/2].

The Cosine Function and Its Inversecos(cos-1 x) = x for every x in the interval [-1, 1]. cos-1(cos x) = x for every x in the interval [0, ].

The Tangent Function and Its Inversetan(tan-1 x) = x for every real number x tan-1(tan x) = x for every x in the interval (-/2,/2).

• Find the exact value, if possible.

Examples

7.0coscos 1

sinsin 1

Ask this question: Is the value of x in the domain of ?

x1cos

Is the value of x in the domain of ? If not, then we must evaluate first.

x1sin

sin

2.1coscos 1

Find the exact value of

Example 1- Evaluating a Composite Trig Expression

Use a right triangle to write the expression as an algebraic expression.

Example 4