Arcsin Calculator

The arcsin function, also known as the inverse sine, is a mathematical tool used to determine the angle whose sine is a given number. In simpler terms, if you know the sine value of an angle, arcsin helps you find the angle itself.

What Is Arcsin?

Arcsin is the inverse operation of the sine function. The sine function takes an angle and returns its sine value (a ratio). The arcsin function does the opposite—it takes a sine value and gives back the angle.

Arcsin Formula

The arcsin function is typically written as:

\[
\text{arcsin}(x) = y \quad \text{where } \sin(y) = x, \, -1 \leq x \leq 1, \, -\frac{\pi}{2} \leq y \leq \frac{\pi}{2}.
\]

• \( x \): Sine value (input).
• \( y \): Angle in radians or degrees (output).

How the Arcsin Calculator Works

An arcsin calculator automates the process of finding angles. Here’s how it functions:

1. Input a Sine Value: Enter a number between -1 and 1.
2. Choose a Unit: Select radians or degrees for the output.
3. Get the Angle: The calculator will instantly compute the angle.

Example Use

Imagine you know the sine value of an angle is \( 0.5 \), and you want to find the angle:

1. Enter \( 0.5 \) into the calculator.
2. Select “degrees” as the output unit.
3. The result will be 30°, because \(\sin(30^\circ) = 0.5\).

Arcsine (Inverse Sine) Table

Below is a table showing common sine values and their corresponding angles in degrees and radians for quick reference:

How to Use This Table

1. Locate the sine value (\( x \)) in the first column.
2. Find the corresponding angle in degrees or radians from the other columns.
3. Use this information for quick trigonometric calculations without needing a calculator.

Example:

If the sine value is \( 0.5 \), the corresponding angle is:

• 30° in degrees.
• \( \frac{\pi}{6} \) in radians.

This table is a useful tool for solving trigonometric problems, especially in geometry, physics, and engineering.