inverse trigonometry functions and their derivatives · θ = sec-1x tan (sec-1x) = 7 csc ex 3...
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Inverse Trigonometry Functionsand Their Derivatives
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The graph of y = sin x does not pass the horizontal line test, so it has no inverse.
If we restrict the domain (to half a period), then we can talk about an inverse function.
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Definition
notation
EX 1 Evaluate these without a calculator.
a) c)
b) d)
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y = tan x y = sec x
Definition
[ ]
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EX 2 Evaluate without a calculator.
a) b) c)
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1
xθ
θ = cos-1x
sin(cos-1x) =
x
1θ sec (tan-1x) =
θ = tan-1x
x
1θ
θ = sec-1x
tan (sec-1x) =
7
csc
EX 3 Calculate sin[2cos-1(1/4)] with no calculator.
Derivatives of Inverse Trig Functions
Let y = cos-1x. Find y'.
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C
C
EX 4
EX 5 Evaluate these integrals.
a)
b)
∈
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