Question

Use complete sentences to describe the range of the sine function.

Answer 1

The Range of a function is the set of all values that that function can take.

Given the sine function f(x)=sinx,

This function is the function which calculates the sine of the values of x.

According to the definition of the sine of an angle x in the unit circle, 

$-1 \leq sinx \leq 1$,

so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.

This means that the values that the sine function takes are any values between -1 and 1, inclusive.

This determines the Range of the sine function. 

So the Range of the sine function is [-1, 1]