Inverse Trigonometric Functions Worksheets With Answers Page 2
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24INVERSE TRIGONOMETRIC FUNCTIONS
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(iii) Whenever no branch of an inverse trigonometric function is mentioned, we mean
the principal value branch. The value of the inverse trigonometic function which
lies in the range of principal branch is its principal value.
2.1.2 Graph of an inverse trigonometric function
The graph of an inverse trigonometric function can be obtained from the graph of
original function by interchanging x-axis and y-axis, i.e, if (a, b) is a point on the graph
of trigonometric function, then (b, a) becomes the corresponding point on the graph of
its inverse trigonometric function.
It can be shown that the graph of an inverse function can be obtained from the
corresponding graph of original function as a mirror image (i.e., reflection) along the
line y = x.
2.1.3 Properties of inverse trigonometric functions
–
,
sin
(sin x) = x
:
x
–1
1.
2 2
cos
(cos x) = x
:
[0, ]
–1
x
⎛
⎞
–π π
∈ ⎜
,
⎟
x
tan
–1
(tan x) = x
:
⎝
2 2
⎠
(
)
x ∈
cot
(cot x) = x
:
0, π
–1
π
[0, π] –
sec
(sec x) = x
:
x
–1
2
–π π
,
– {0}
x
cosec
–1
(cosec x) = x :
2 2
x ∈[–1,1]
sin (sin
–1
x) = x
:
2.
x ∈[–1,1]
cos (cos
x) = x
:
–1
x ∈R
tan (tan
x) = x
:
–1
x ∈R
cot (cot
x) = x
:
–1
x ∈R – (–1,1)
sec (sec
x) = x
:
–1
x ∈R – (–1,1)
cosec (cosec
x) = x :
–1
1
–1
–1
sin
cosec x
x ∈R – (–1,1)
:
3.
x
1
–1
–1
cos
sec x
x ∈R – (–1,1)
:
x
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