We are asked to fill in the blanks to complete the information about the inverse sine function.
Function
Alternative Notation
Domain
Range
y=arcsin x
- π/2 ≤ y ≤ π/2
Let's start by recalling that on the restricted domain - π2 ≤ x ≤ π2, the function y=sin x is one-to-one and has a unique inverse function. This function is called the inverse sine function and is denoted by y=arcsin x or y=sin ^(- 1) x. It is defined by y=arcsin x if and only if sin y=x where - 1≤ x ≤ 1 and - π2 ≤ y ≤ π2. Let's take a look at the graph of y=arcsin x.
We can see that the domain of y=arcsin x is - 1≤ x ≤ 1 and the range is - π2 ≤ y ≤ π2. Now we can fill in the blanks.
