1. Inverse Trigonometric Functions
Digital Lesson
Inverse Trigonometric Functions

2. Inverse Sine Function
Recall that for a function to have an inverse, it must be a one-to-one function and pass the Horizontal Line Test.
f(x) = sin x does not pass the Horizontal Line Test
and must be restricted to find its inverse. y x
y = sin x
Sin x has an inverse function on this interval.
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Inverse Sine Function

3. Example: Angle whose sine is x This is another way to write arcsin x.
Angle whose sine is x
Example:
This is another way to write arcsin x.
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Inverse Sine Function

4. Inverse Cosine Function
f(x) = cos x must be restricted to find its inverse. y x
y = cos x
Cos x has an inverse function on this interval.
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Inverse Cosine Function

5. Inverse Cosine Function
Angle whose cosine is x
Example:
This is another way to write arccos x.
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Inverse Cosine Function

6. Inverse Tangent Function
f(x) = tan x must be restricted to find its inverse. y x
y = tan x
Tan x has an inverse function on this interval.
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Inverse Tangent Function

7. Inverse Tangent Function
Angle whose tangent is x
The domain of y = arctan x is
Example:
This is another way to write arctan x.
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Inverse Tangent Function

8. Graphing Utility: Graphs of Inverse Functions
Graphing Utility: Graph the following inverse functions.
Set calculator to radian mode.
–1.5
1.5 – 
a. y = arcsin x
–1.5
1.5 2 –
b. y = arccos x –3 3  –
c. y = arctan x
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Graphing Utility: Graphs of Inverse Functions

9. Graphing Utility: Inverse Functions
Graphing Utility: Approximate the value of each expression.
Set calculator to radian mode.
a. cos–1 0.75
b. arcsin 0.19
c. arctan 1.32
d. arcsin 2.5
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Graphing Utility: Inverse Functions