1. What is Inverse Cosine?

The inverse cosine (arccos) function calculates the angle whose cosine is a given value. It's the inverse operation of the cosine function, returning angles typically in the range [0, π] radians or [0°, 180°].

2. How Does the Calculator Work?

The calculator uses the inverse cosine function:

Where:

• \( \theta \) — Resulting angle (degrees or radians)
• \( x \) — Input value (-1 ≤ x ≤ 1)

Explanation: The function returns the principal value of the angle whose cosine equals the input value x. The output can be in degrees or radians.

3. Importance of Inverse Cosine

Details: Inverse cosine is essential in trigonometry, physics, engineering, and computer graphics for determining angles from cosine values, solving triangles, and calculating rotations.

4. Using the Calculator

Tips: Enter a value between -1 and 1, select your preferred output unit (degrees or radians). The calculator will return the corresponding angle.

5. Frequently Asked Questions (FAQ)

Q1: Why must the input be between -1 and 1?
A: The cosine function only produces values in this range, so its inverse is only defined for these inputs.

Q2: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 units, while radians use 2π (about 6.283) units. Radians are often preferred in advanced mathematics.

Q3: Can I get angles beyond 180°?
A: The principal value of arccos is always between 0° and 180° (0 and π radians). Other solutions would be found using trigonometric identities.

Q4: How precise are the calculations?
A: The calculator uses PHP's built-in acos() function which provides high precision (about 14 decimal places).

Q5: What are common applications of inverse cosine?
A: Used in navigation, physics (e.g., calculating angles between vectors), computer graphics (rotations), and engineering (mechanical systems).