What is the domain and range of y=arcsin⁡x

Deragz

Deragz

Answered

2021-12-26

What is the domain and range of y=arcsinx

Answer & Explanation

Mary Herrera

Mary Herrera

Expert

2021-12-27Added 37 answers

Range: -pi/2 ≤ y ≤ pi/2
Domain: -1 ≤ x ≤ 1
lenkiklisg7

lenkiklisg7

Expert

2021-12-28Added 29 answers

More explanation please
user_27qwe

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 y=sinx an interval of monotonic behavior is usually chosen as [π2,π2], where the function is monotonously increasing from -1 to 1.
This variant of a sine function, reduced to an interval where it is monotonous and fills an entire range, has an inverse function called y=arcsin(x)
It has range [π2,π2] and domain from -1 to 1

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