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On what interval is the identity sin^-1(sin (x)) = x valid?

User Rbarni
by
8.3k points

1 Answer

1 vote

Answer:

It is valid in the interval
[(-\pi )/(2),(+\pi )/(2)]

Explanation:

Let
f(x)=sin^(-1)(sin(x))

The domain of the given function is


sin(x)\in [-1,1]\\\\(\because sin^(-1)xis defined only for x in the set[-1,+1])

Thus we have


-1\leq sin(x)\leq +1\\\\\Rightarrow sin^(-1)(-1)\leq sin^(-1)(sin(x))\leq sin^(-1)1\\\\\therefore (-\pi )/(2)\leq sin^(-1)(sin(x))\leq (+\pi )/(2)\\


\therefore x\in [-\pi /2,+\pi /2]

User Xpleria
by
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