Arcsin 0 equals 0 because the arcsine function is the inverse of the sine function, and sin 0 = 0.
Understanding the Arcsine Function
The arcsine function, denoted as arcsin(x) or sin-1(x), answers the question: "What angle has a sine of x?" In other words, it's the inverse function of the sine.
- Sine Function: The sine function (sin θ) takes an angle (θ) as input and returns a value between -1 and 1.
- Arcsine Function: The arcsine function takes a value between -1 and 1 as input and returns an angle (usually in radians) whose sine is that value.
The Relationship Between Sine and Arcsine
Because arcsine is the inverse of sine:
- If sin(θ) = x, then arcsin(x) = θ
Why arcsin 0 = 0
We know that sin(0) = 0. Therefore, using the inverse relationship:
- arcsin(0) = 0
This means that the angle whose sine is 0 is 0 radians (or 0 degrees).
In essence, arcsin 0 = 0 because the sine of 0 is 0, and the arcsine function finds the angle that gives you a specific sine value.
