Deragz

Answered

2021-12-26

What is the domain and range of $y=\mathrm{arcsin}x$

Answer & Explanation

Mary Herrera

Expert

2021-12-27Added 37 answers

Range: -pi/2 ≤ y ≤ pi/2

Domain: -1 ≤ x ≤ 1

Domain: -1 ≤ x ≤ 1

lenkiklisg7

Expert

2021-12-28Added 29 answers

More explanation please

user_27qwe

Expert

2021-12-30Added 230 answers

The original sine function defined for any real argument does not have an inverse function because it does not establish a one-to-one correspondence between its domain and a range.

To be able to define an inverse function, we have to reduce the original definition of a sine function to an interval where this correspondence does take place. Any interval where sine is monotonic and takes all values in its range would fit this purpose.

For a function

This variant of a sine function, reduced to an interval where it is monotonous and fills an entire range, has an inverse function called

It has range

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