What are the Inverse Trigonometric Functions?

What are the Inverse Trigonometric Functions?

The inverse of a function f : A → B exists if f is one-one onto i.e., a bijection and is given by f(x) = y ⇒ f-1(y) = x.

Graphs of inverse trigonometric functions

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Domain and Range of inverse trigonometric functions

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Properties of inverse trigonometric functions

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(5) Principal values for inverse circular functions:
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(6) Conversion property:
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(7) General values of inverse circular functions:
We know that if ?  is the smallest angle whose sine is x, then all the angles whose sine is x can be written as nx + (−1)n? where n = 0, 1, 2, ……. Therefore, the general value of sin1 x can be taken as nx + (−1)n?. The general value of sin1 x is denoted by sin1 x.
Thus, we have
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Similarly, general values of other inverse circular functions are given as follows:
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Formulae for sum, difference of inverse trigonometric function

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Inverse trigonometric ratios of multiple angles

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