1. What is Inverse Cosine (arccos)?

The inverse cosine function (arccos) returns the angle whose cosine is the given number. The result is in radians and ranges from 0 to π (0 to 180 degrees).

2. How Does the Calculator Work?

The calculator uses the inverse cosine function:

Where:

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

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

3. Importance of Inverse Cosine Calculation

Details: Inverse cosine 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. The calculator will return the angle in radians (0 to π).

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid inputs?
A: The input (x) must be between -1 and 1, inclusive. This is the range of the cosine function.

Q2: How do I convert the result to degrees?
A: Multiply the radians result by (180/π) ≈ 57.2958 to convert to degrees.

Q3: Why does arccos return values between 0 and π?
A: This is the principal value range where each cosine value corresponds to exactly one angle.

Q4: What happens if I enter a value outside [-1, 1]?
A: The function is undefined for values outside this range. The calculator will not return a result.

Q5: What are some practical applications of arccos?
A: Used in navigation, robotics, computer graphics (lighting calculations), and signal processing.