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Inverse Trigonometry - make it easy
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Key NotesChapter-02
Inverse Trigonometric Functions
• The domains and ranges (principal value branches) of inverse trigonometric functions are
given in the following table:
Functions Domain Range (Principal Value Branches)
y = sin−1x [-1, 1] −π π
2 , 2
y = cos −1 x [-1, 1] [ 0, π]
y = cos ec−1x R- [-1, 1] −π π
2 , 2 -{0}
y = sec−1 x R-[-1, 1] π
[0, π] − { }
2
y = tan −1 x R π π
− 2 , 2
y = cot −1 x R [ 0, π]
1
sin −1x should not be condused with (sin x) −1 . In fact (sin x)−1 = And similarly for other
sin x
trigonometric functions
• The value of an inverse trigonometric functions which lies in its principal value branch is
called the principal value of that inverse trigonometric functions.
For suitable values of domain, we have
• y = sin −1 x ⇒ x = sin y
• x = sin y ⇒ y = sin −1 x
• sin (sin −1 x) = x
• sin −1 (sin x) = x
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