1. What is Arccosine Function?

The arccosine function (cos⁻¹ or acos) is the inverse of the cosine function. It returns the angle whose cosine is the given number. The output range is [0, π] radians or [0°, 180°].

2. How Does the Calculator Work?

The calculator uses the mathematical function:

Where:

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

Explanation: The arccosine function finds the angle whose cosine equals the input value x. The result is always between 0 and π radians (0° and 180°).

3. Importance of Arccosine Calculation

Details: Arccosine is essential in trigonometry, physics, engineering, and computer graphics for converting between cosine values and angles. It's used in vector calculations, signal processing, and solving trigonometric equations.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the domain and range of arccosine?
A: Domain: [-1, 1], Range: [0, π] radians or [0°, 180°].

Q2: Why is the output range limited to 0-180 degrees?
A: This ensures the function is one-to-one and has a unique output for each input, making it mathematically well-defined.

Q3: How is arccosine different from arcsin and arctan?
A: Arccosine finds angles from cosine values, arcsin from sine values, and arctan from tangent values. Each has different domains and ranges.

Q4: Can I calculate arccosine for values outside [-1,1]?
A: No, since cosine values are always between -1 and 1, arccosine is only defined for inputs in this range.

Q5: When should I use radians vs degrees?
A: Use radians for mathematical calculations and programming, degrees for everyday applications and geometry problems.