Domain & range of inverse functions
Note :
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o sin – 1 x should not be confused with ( sin x ) – 1 . In fact ( sin x ) – 1 = 1 / sin x and similarly for other trigonometric functions .
Whenever no branch of inverse trigonometric functions is mentioned , we mean the principal value branch of that function .
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The value of an inverse trigonometric functions which lies in the range of principal branch is called the principal value of that inverse trigonometric functions
Domain & range of inverse functions
Numerical : Find sin – 1 ( -1 / 2 ) Solution : sin – 1 ( -1 / 2 ) = y Sin y = -1 / 2 = sin ( -π / 6 )
Or y = -π / 6