Question

The domain for arcsine (arcsin) is __, and the range is __.

A. [-π/2, π/2] for both domain and range.
B. [-1,1] for the domain and [-π/2, π/2] for the range.
C. [-1,1] for both domain and range.
D. [0, π] for the domain and [0, π] for the range.

Answer 1

The domain for arcsine (arcsin) is [-1,1], and the range is [-π/2, π/2], which indicates that option B is the correct answer.

Step-by-step explanation:

The domain for arcsine (arcsin) is [-1,1], and the range is [-π/2, π/2]. The correct answer to this question is option B. The function arcsine is the inverse of the sine function. The sine function takes an angle as an input and outputs a numerical value between -1 and 1. Therefore, when we apply arcsine, we are referring to the inverse process, where the input must be a value within the range of sine, which is between -1 and 1, and the output is the angle that corresponds to this sine value, which will always be between -π/2 and π/2, based on the unit circle. This is why the domain of arcsin is limited to values between -1 and 1 since these are the only values for which an angle with that sine exists in real numbers.