1. What is the Inverse Cosine Function?

The inverse cosine function (arccos) returns the angle whose cosine is the given number. It's the inverse operation of the cosine function, returning values between 0 and π radians (0° to 180°).

2. How Does the Calculator Work?

The calculator uses the inverse cosine formula:

Where:

• \( \theta \) — The resulting angle (in radians or degrees)
• \( x \) — Input value (must be between -1 and 1)

Explanation: The function calculates the principal value of the angle whose cosine equals the input value.

3. Importance of Inverse Cosine

Details: The inverse cosine function is essential in trigonometry, physics, engineering, and computer graphics for determining angles from cosine values.

4. Using the Calculator

Tips: Enter a value between -1 and 1, select whether you want the result in radians or degrees. The calculator will return the principal value of the angle.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the difference between radians and degrees?
A: Radians (0 to π) and degrees (0° to 180°) are different units for measuring angles. Radians are often preferred in mathematical calculations.

Q3: What is the principal value?
A: The arccos function returns the smallest non-negative angle (between 0 and π) that satisfies the equation.

Q4: Can I calculate inverse cosine for complex numbers?
A: This calculator only handles real numbers. Complex number calculations would require a different approach.

Q5: How precise are the results?
A: Results are accurate to at least 4 decimal places, using PHP's built-in acos() function.