1. What is the Cosine Formula in Trigonometry?

Definition: The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the hypotenuse.

Purpose: This fundamental trigonometric relationship helps solve problems in geometry, physics, engineering, and navigation.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \cos(\theta) \) — Cosine of angle θ (dimensionless)
• Adjacent — Length of side adjacent to angle θ (meters)
• Hypotenuse — Longest side of right triangle (meters)

Explanation: The calculator first computes the cosine ratio, then determines the angle in degrees using the inverse cosine function.

3. Importance of the Cosine Function

Details: The cosine function is essential for calculating angles and distances in right triangles, modeling periodic phenomena, and vector analysis.

4. Using the Calculator

Tips: Enter the lengths of the adjacent side and hypotenuse (both must be positive values). The hypotenuse must be equal to or longer than the adjacent side.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of possible cosine values?
A: Cosine values always range between -1 and 1 for any angle.

Q2: Why does my calculator show an error?
A: This happens if the hypotenuse is shorter than the adjacent side, which violates the Pythagorean theorem.

Q3: How accurate are the results?
A: Results are accurate to 6 decimal places for cosine and 2 decimal places for angles.

Q4: Can I use different units?
A: Yes, as long as both measurements use the same units (e.g., both in cm or both in feet).

Q5: What if I know the angle and want to find sides?
A: Use our other trigonometry calculators for those calculations.