1. What is Arccos (Cos⁻¹)?

The arccosine function (arccos or cos⁻¹) is the inverse of the cosine function. It takes a ratio (between -1 and 1) and returns the angle whose cosine is that ratio. This is useful for finding angles when you know the cosine value.

2. How Does the Calculator Work?

The calculator uses the mathematical arccosine function:

Where:

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

Explanation: The function calculates the principal value of the angle (between 0 and π radians or 0° and 180° for real inputs).

3. Importance of Inverse Cosine

Details: Arccos is essential in trigonometry, physics, engineering, and computer graphics for determining angles from known ratios. It's particularly important in solving triangles and analyzing periodic phenomena.

4. Using the Calculator

Tips: Enter a value between -1 and 1, select whether you want the result in degrees or radians, and click calculate. The input must be within the valid range for cosine values.

5. Frequently Asked Questions (FAQ)

Q1: Why must the input be between -1 and 1?
A: The cosine of any real angle always produces a value between -1 and 1, so the inverse function is only defined for inputs in this range.

Q2: How do I input cos⁻¹ on my calculator?
A: Typically you press "2nd" or "Shift" followed by the "cos" button. Some calculators may label it as "acos" or "cos⁻¹".

Q3: What's the difference between degrees and radians?
A: Degrees use 360° for a full circle while radians use 2π (about 6.283). Radians are often preferred in higher mathematics.

Q4: Can arccos return multiple answers?
A: Mathematically yes, but calculators return the principal value (0 to π radians or 0° to 180°).

Q5: How is this used in real-world applications?
A: Common uses include calculating angles in navigation, determining phase angles in AC circuits, and solving for unknown angles in geometric problems.