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Precalculus 4-6 Inverse Trig Functions!
Name:_________________________________
Objective: Evaluate and graph inverse trigonometric functions. Find compositions of
trigonometric functions. Common Core Standards: F-IF.5, F-BF.4, F-TF.5, F-TF.6, F-TF.7
W :
Inverse Trig functions can be used to model the changing horizontal angle of rotation needed for a television camera to
follow the motion of drag-racing vehicle.
a. What general characteristics of a function guarantee an inverse to exist and be considered a function?
y
5
4
3
2
b. Draw the inverse of the function below. Label with the correct notation.
c. What IMPORTANT relationships exist between a function f and its inverse?
1
–5
–4
–3
–2
–1
–1
1
2
3
4
–2
–3
–4
–5
d. If cos  
g
, Then cos 1 
h
  _________
e. Can the secant be the inverse of the cosine function?
f.
How could you rewrite sin x to isolate the x, the angle measure?
Why or Why not?
What would x equal?
g. *Remember that one-to-one functions have each y value having only one associated x value.
Some trigonometric functions are not one-to-one functions. Are there portions of the graph of y = sin x that
are one-to-one?
If so, describe one portion of the graph that is one-to-one.
5
x
Inverse relations review
Numerically:
Algebraically:
Geometrically:
Properties of the Inverse Sine Functions (a.k.a arcsin).
Let’s look at the graph of sine and its inverse (arcsin or sin 1 ) *Check with your calculator after.
What is the domain, range for inverse sine if it is one-to-one?
Ex1. Find the exact value of each expression, if it exists.
Properties of the Inverse Cosine Functions (a.k.a arc cosine)
Let’s look at the graph of cosine and its inverse (arcos or cos 1 ). *Check with your calculator after.
What is the domain, range for inverse cosine if it is one-to-one?
Ex 2. Find the exact value of each expression, if it exists.
Properties of the Inverse Tangent Functions (a.k.a arctan)
Let’s look at the graph of inverse tangent:
What is the domain, range for inverse tangent if it is one-to-one?
Ex. 3 Find the exact value of each expression, if it exists.
Ex 4.
Compositions of Trigonometric Functions.
Ex. 6] Find the exact value of ech expression, if it exists.
Ex. 7]. Find the exact value of
Homework:
Day 1: pgs. 288 – 289 #’s 1–10, 15–16.
Day 2: pgs. 288 – 290 #’s 11 – 14, 17–22, 27–37 (odd), 73 – 79.