1. What is the Cosine Function?

The cosine function is a fundamental trigonometric ratio that relates the adjacent side of a right-angled triangle to its hypotenuse. It's widely used in mathematics, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses the cosine formula:

Where:

• \( \cos \theta \) — Cosine of angle θ (dimensionless)
• adjacent — Length of the side adjacent to angle θ (meters)
• hypotenuse — Length of the hypotenuse (meters)

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

3. Importance of Trigonometry

Details: Trigonometric functions like cosine are essential for solving problems involving right triangles, periodic phenomena, waves, circular motion, and many applications in science and engineering.

4. Using the Calculator

Tips: Enter the lengths of the adjacent side and hypotenuse in meters. Both values must be positive numbers, and the hypotenuse must be equal to or longer than the adjacent side.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible cosine values?
A: Cosine values range from -1 to 1. In right triangles (angles between 0° and 90°), cosine values range from 0 to 1.

Q2: What if my hypotenuse is shorter than the adjacent side?
A: This would violate the Pythagorean theorem (hypotenuse must be the longest side). The calculator will not return a valid result in this case.

Q3: Can I use different units of measurement?
A: Yes, as long as both measurements are in the same units. The cosine ratio is dimensionless.

Q4: How accurate is the angle calculation?
A: The angle is calculated to 1 decimal place, which is sufficient for most practical applications.

Q5: What other trigonometric functions are related to cosine?
A: Sine (opposite/hypotenuse) and tangent (opposite/adjacent) are the other primary trigonometric functions.