Inverse Trigonometric Functions Worksheets With Answers
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Chapter
INVERSE TRIGONOMETRIC
FUNCTIONS
2.1 Overview
2.1.1 Inverse function
Inverse of a function ‘f ’ exists, if the function is one-one and onto, i.e, bijective.
Since trigonometric functions are many-one over their domains, we restrict their
domains and co-domains in order to make them one-one and onto and then find
their inverse. The domains and ranges (principal value branches) of inverse
trigonometric functions are given below:
Functions
Domain
Range (Principal value
branches)
–π π
,
y = sin
[–1,1]
–1
x
2 2
y = cos
[–1,1]
[0,π]
–1
x
–π π
,
– {0}
y = cosec
R– (–1,1)
–1
x
2 2
π
y = sec
R– (–1,1)
[0,π] –
–1
x
2
–π π
,
y = tan
–1
x
R
2 2
y = cot
–1
(0,π)
x
R
Notes:
(i) The symbol sin
x should not be confused with (sinx)
. Infact sin
x is an
–1
–1
–1
angle, the value of whose sine is x, similarly for other trigonometric functions.
The smallest numerical value, either positive or negative, of θ is called the
(ii)
principal value of the function.
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