For a function to have an inverse, it must be one-to-one_. To define the inverse sine function, we restrict the domain of the sine function to the interval [-pi, pi].
Two functions f(x) and g(x) are inverses if:
f(x) = y
g(y) = x
This means that the two functions need to be one-to-one, because if there are two values of x such that:
f(x₁) = y = f(x₂)
f(x) can't have an inverse because g(y) would give two different outputs, and then g(x) is not a function.
For the case of the sine (and all periodic functions) we restrict to the region where the function is one to one, which can be any interval of 2 pi radians (the common example is the interval [-pi, pi])
Then:
For a function to have an inverse, it must be one-to-one_. To define the inverse sine function, we restrict the domain of the sine function to the interval [-pi, pi].
If you want to learn more about inverse functions:
https://brainly.com/question/14391067
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