Download PCH Notes 4.7c

Date:
4.7(c) Notes: Compositions of Functions
Lesson Objective: To evaluate and graph the
compositions of trig function.
CCSS: F-TF Extend the domain of trigonometric
functions using the unit circle.
You will need: unit circle
This is Jeopardy!:
Lesson 1: Evaluating Compositions of Functions
If f(x) = 2x, what is f -1(x)?
What is f(f -1(x))?
What is f -1(f(x))?
Lesson 1: Evaluating Compositions of Functions
Inverse Properties:
Function within:
Only if x falls:
sin(sin-1x) = x
sin-1(sin x) = x
[-1, 1]
[-π/2, π/2]
cos(cos-1x) = x
cos-1(cos x) = x
[-1, 1]
[0, π]
tan(tan-1x) = x
tan-1(tan x) = x
(-∞, ∞)
(-π/2, π/2)
Lesson 1: Evaluating Compositions of Functions
Find the exact value, if possible.
2
-1
cos(cos
)
A.
=
2
B. sin-1(sin π) =
C. cos(cos-1 -1.2) =
Lesson 2: Evaluating a Composite Trig
Expression
Evaluate.
A. cos[sin-1(-½)] =
B. sin[tan-1(1)] =
Lesson 3: Using a Sketch to Evaluate Composite
Trig Expressions
Use a sketch to find the exact values.
A. sin[tan-1 (¾)]
B. cot[sin-1 (- 5/13)]
Lesson 4: Simplifying Trig Expressions as an
Algebraic Expression
Use a right triangle to write each expression as
an algebraic expression. Assume that x is positive and that the given inverse trig function is
defined for the expression in x.
A. sin(cos-1 2x)
B. sec(tan-1 x)
4.7(c): Do I Get It? Yes or No
1. Find the exact value, if possible.
a. cos(cos-1 0.6) b. sin-1(sin 3π/2) c. cos(cos-1 1.5)
2. Use a sketch to find the exact values.
a. cos(tan-1 5/12) b. cot[sin-1(-⅓)]
3. Use a right triangle to write each expression as an algebraic expression. Assume that x
is positive and that the given inverse trig
function is defined for the expression in x.
a. cos(sin-1 x)
b. sin(tan-1 x)
4. Find the exact value of cos-1(sin 2π/3).
4.7(c): Do I Get It? Yes or No
Answers:
1.
2.
3.
4.
a. 0.6
b. - π/2 c. not defined
a. 12/13 b. -2 √2
a. √(1 – x2)
b. x√(x2 + 1)
x2 + 1
π/
6