Question

The range of y = Arcsin x is [ -pi/2, pi/2]
T/F​

Answer 1

True

`\textrm{Range of arcsin(x) is } \left[-(\pi )/(2),\:(\pi )/(2)\right]`

Explanation:

The maximum value of sin(x) is 1 and occurs when x =
`(\pi)/(2)`

The minimum value of sin(x) is - 1 and occurs when x =
`-(\pi)/(2)`

If we taken the inverse of sin(x) which is arcsin(x) then the range should be the x value range for sin(x) i.e.
`\left[-(\pi )/(2),\:(\pi )/(2)\right]`