1. What is the Cosine Function?

The cosine function relates the adjacent side and hypotenuse of a right-angled triangle. It's one of the primary trigonometric functions and is fundamental in geometry, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the cosine formula:

Where:

• \( \theta \) — Angle between adjacent side and hypotenuse
• Adjacent Side — Side next to the angle θ
• Hypotenuse — Longest side of the right triangle

Explanation: The cosine value ranges between 0 and 1 for angles between 0° and 90° in a right triangle.

3. Importance of Cosine Calculation

Details: Cosine is essential for solving right triangles, analyzing periodic phenomena, signal processing, and in many physics applications involving waves and oscillations.

4. Using the Calculator

Tips: Enter lengths of adjacent side and hypotenuse (must be positive values and hypotenuse ≥ adjacent side). The calculator will compute both the cosine value and the corresponding angle.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of cosine values?
A: In a right triangle, cosine values range from 0 (90° angle) to 1 (0° angle).

Q2: Can hypotenuse be shorter than adjacent side?
A: No, in a right triangle, the hypotenuse is always the longest side.

Q3: What if I get an error message?
A: Ensure hypotenuse ≥ adjacent side and both values are positive. The calculator validates inputs automatically.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places for cosine and 1 decimal place for angles.

Q5: Can I use this for non-right triangles?
A: No, this calculator is specifically for right-angled triangles. For other triangles, use the Law of Cosines.