1. What is Inverse Cosine?

The inverse cosine (arccosine) function calculates the angle whose cosine is a given number. This calculator returns the angle in degrees, which is more commonly used in practical applications than radians.

2. How Does the Calculator Work?

The calculator uses the inverse cosine formula:

Where:

• \( \theta \) — Angle in degrees
• \( x \) — Input value (must be between -1 and 1)
• \( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The calculator first computes the arccosine in radians, then converts the result to degrees by multiplying by 180/π.

3. Understanding the Results

Range: The inverse cosine function returns values between 0° and 180° (0 and π radians). For negative inputs, the angle will be in the second quadrant (between 90° and 180°).

4. Using the Calculator

Tips: Enter any value between -1 and 1. The calculator will return the corresponding angle in degrees. Values outside [-1, 1] are invalid as cosine values must be in this range.

5. Frequently Asked Questions (FAQ)

Q1: Why use degrees instead of radians?
A: Degrees are more intuitive for most practical applications in navigation, engineering, and everyday measurements.

Q2: What's the difference between arccos and cos⁻¹?
A: They are the same function, just different notations. Both represent the inverse cosine function.

Q3: What are common values to know?
A: arccos(1) = 0°, arccos(0) = 90°, arccos(-1) = 180°, arccos(0.5) = 60°, arccos(√2/2) = 45°.

Q4: Can I calculate inverse cosine for values outside [-1, 1]?
A: No, the cosine function only produces values between -1 and 1, so its inverse is only defined for this range.

Q5: How precise is this calculator?
A: The calculator uses PHP's built-in acos() function which provides high precision, with results rounded to 4 decimal places.