Inverse Cosine Calculator

How to Calculate Inverse Cosine (arccos)

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

Formula

The inverse cosine function is denoted as:

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

Where:

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

Calculation Steps

1. Ensure the input value x is between -1 and 1 (inclusive).
2. Use the arccos 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 arccos(0.5):

1. Input: x = 0.5
2. Calculate arccos(0.5): \[ \theta = \arccos(0.5) \approx 1.0472 \text{ radians} \]
3. Convert to degrees: \[ 1.0472 \text{ radians} \times \frac{180°}{\pi} \approx 60° \]

Therefore, arccos(0.5) ≈ 1.0472 radians or 60°.

Visual Representation

This diagram illustrates arccos(0.5). The blue arc represents the angle of 60°, and the red line shows the cosine value of 0.5 on the unit circle.