1. What is Inverse Cosine?

The inverse cosine function (arccos) is the inverse of the cosine function. It returns the angle whose cosine is the given number. The output is in radians (or can be converted to degrees) between 0 and π radians (0° to 180°).

2. How Does the Calculator Work?

The calculator uses the inverse cosine function:

Where:

• \( x \) — Input value (must be between -1 and 1)
• \( \theta \) — Output angle in radians

3. Mathematical Explanation

Domain: The arccos function is defined only for x values between -1 and 1.
Range: The output angle is always between 0 and π radians (0° to 180°).
Principal Value: The calculator returns the principal value of arccos.

4. Using the Calculator

Tips: Enter a value between -1 and 1. The calculator will return the angle in both radians and degrees. Invalid inputs will be rejected.

5. Frequently Asked Questions (FAQ)

Q1: Why is the input limited to -1 to 1?
A: The cosine of any angle always produces values between -1 and 1, so the inverse is only defined in this range.

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

Q3: How is the degree conversion calculated?
A: Degrees = radians × (180/π). The calculator performs this conversion automatically.

Q4: What about angles in other quadrants?
A: The arccos function returns only the principal value (0 to π radians). For other solutions, trigonometric identities must be used.

Q5: Can I calculate inverse cosine for complex numbers?
A: This calculator handles only real numbers. Complex number calculations would require more advanced mathematics.