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Question

What is the fundamental period of the function y=sin−1(sinx).

A
2π
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B
4π
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C
3π
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D
π
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Solution

The correct option is A 2π
f(x)=sin1(sinx).
Domain of f(x) is R and sin x is periodic. Hence f(x)=sin1(sinx) is also periodic. Here we can make use of the graph to visualise the periodicity of the function.
Since sin(x) has a period of 2π,sin1(sinx) also has a period of 2π. The graph below shows the functions y=sin1(sinx) and y = sin x.

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