Inverse Sine Calculator

How to Calculate Inverse Sine (arcsin)

The inverse sine function, also known as arcsin or sin⁻¹, is used to find the angle whose sine is a given value. It's the inverse operation of the sine function.

Formula

The inverse sine function is denoted as:

\[ \theta = \arcsin(x) \]

Where:

• θ is the angle in radians
• x is the sine value (-1 ≤ x ≤ 1)

Calculation Steps

1. Ensure the input value x is between -1 and 1 (inclusive).
2. Use the arcsin function to calculate the angle in radians.
3. If needed, convert the result to degrees using the formula: degrees = radians × (180/π).

Example

Let's calculate arcsin(0.5):

1. Input: x = 0.5
2. Calculate arcsin(0.5): \[ \theta = \arcsin(0.5) \approx 0.5236 \text{ radians} \]
3. Convert to degrees: \[ 0.5236 \text{ radians} \times \frac{180°}{\pi} \approx 30° \]

Therefore, arcsin(0.5) ≈ 0.5236 radians or 30°.

Visual Representation

This diagram illustrates arcsin(0.5). The blue arc represents the angle of 30°, and the red line shows the sine value of 0.5 on the unit circle.