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
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