1. What is Arccosine?

Arccosine (arccos or cos⁻¹) is the inverse trigonometric function of cosine. It returns the angle whose cosine is the given number. The output is typically in radians or degrees, ranging from 0 to π radians (0° to 180°).

2. How Does the Calculator Work?

The calculator uses the arccosine formula:

Where:

• \( \theta \) — The angle in degrees
• \( \text{adjacent} \) — Length of the side adjacent to the angle
• \( \text{hypotenuse} \) — Length of the hypotenuse

Explanation: The calculator computes the ratio of adjacent to hypotenuse, then calculates the inverse cosine to find the angle in degrees.

3. Importance of Arccosine Calculation

Details: Arccosine is essential in trigonometry, geometry, physics, engineering, and computer graphics for determining angles from known side lengths in right triangles.

4. Using the Calculator

Tips: Enter positive values for both adjacent and hypotenuse lengths. The adjacent side must be less than or equal to the hypotenuse. The calculator returns the angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of arccosine values?
A: Arccosine returns values between 0° and 180° (0 and π radians).

Q2: When is arccosine undefined?
A: Arccosine is undefined when the ratio is outside the range [-1, 1]. In a right triangle context, this means adjacent > hypotenuse is invalid.

Q3: Can arccosine be used for non-right triangles?
A: The arccosine function itself is general, but the adjacent/hypotenuse ratio specifically applies to right triangles.

Q4: How accurate is the calculation?
A: The calculation uses PHP's built-in acos() function, which provides high precision results.

Q5: What units does the calculator use?
A: The calculator returns angles in degrees. The input lengths can be in any consistent units (cm, m, inches, etc.).