Math

Explain why domain restrictions for inverse trigonometric functions are necessary?

I’m having trouble understanding this topic could anyone explain? My teacher makes no sense :/

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  1. take a look at a standard sine function and its inverse
    i.e. y = sin x and y = arcsin x

    you will notice, just like the inverse of any function, that one is a reflection of the other in the line y = x
    (your teacher must have pointed that out)

    which means that the domain function becomes the range of its inverse, and the range of the function becomes the range of its inverse

    since the range of y = sin(x) is -1 ≤ y ≤ 1
    the domain of the inverse function is -1 ≤ x ≤ 1

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