Inverse Trigonometric Functions

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InverseTrigonometric Functions
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OBJECTIVES

• Evaluate the inverse sine function
• Evaluate the other inverse trig functions
• Evaluate the compositions of trig functions

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Inverse Sine Wave
The inverse sine function is defined by y
arcsin x if and only if sin y x
Question
How would you restrict the domain of the sine
function to get the full range of values and have
the graph pass the horizontal line test?
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Inverse Sine Wave
Does your restriction on the domain of the sine
function match the range of the inverse sine wave?
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Domain and Range of Arcsin (Inverse Sine)

• Domain

Range
Notice
The domain of arcsine is the same as the range
of sine.
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Questions??

• If possible, find the exact value.

• arcsin
• sin-1
• sin-1 2

Not possible WHY????

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Inverse Cosine Function

• Inverse Cosine (arccos)

Domain -1 x 1
Range 0 y
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Inverse Tangent function
Domain - lt x lt Range
lt y lt
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Questions??

• If possible, find the exact value.

• arccos
• tan-1 0
• cos-1 (-1)

0


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Real-World Example
a.)
Solving for theta
b.)
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Compositions of Trig Functions
The Domain (x) and Range (y) of each
function still applies.
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Examples
a.
b.