The Inverse Sine, Cosine, and Tangent Functions

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Section 7.1 The Inverse Sine, Cosine, and Tangent
Functions
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Use of Inverses
Inverse functions are foundational for solving
equations. You use inverse functions to move
expressions from one side of the equation to the
other.
The inverse of adding 7 is subtracting 7
The inverse of multiplying by 3 is dividing by
3
The inverse of squaring is square rooting
except that the squaring function really doesnt
have an inverse, so we find a way to use the
square root function to give us all the solutions.
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It fails. This function has no inverse.
Horizontal line test
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Restricted domain
The blue function has an inverse. This inverse
function is
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Review of Properties of Functions and Their
Inverses
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y sin x
It fails. This function has no inverse.
Horizontal line test
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Restrict the Domain
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Domain
Range
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Find the angle ? so that sin ? 1.
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On the unit circle, where (in quadrants 4 and 1)
is y equal to 1?
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Find the angle ? so that sin ? -1/2.
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On the unit circle, where (in quadrants 4 and 1)
is y equal to -1/2 ?
1/2
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whenever you can compute the inverse sine.
gives you either a positive angle in Q1 or a
negative angle in Q4.
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The angle is a positive angle in Q1. p/8.
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0.5
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Find the angle ? so that cos ? 0.
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Find the angle ? so that
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The function cos1 gives an angle in Q1 or Q2.
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The function tan1 gives the same kinds of angles
as sin1 does.
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Domain of f all real numbers (misleading,
because this f has no inverse!)
Domain of f 1 3, 1
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