1. What is the Cosine Formula?

The cosine formula in a right triangle relates the angle θ to the ratio of the adjacent side to the hypotenuse. It's one of the fundamental trigonometric functions used in geometry, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the cosine formula:

Where:

• \( \cos(\theta) \) — Cosine of angle θ (unitless ratio)
• Adjacent Side — Side next to angle θ (length units)
• Hypotenuse — Longest side opposite the right angle (length units)
• θ — Angle between adjacent side and hypotenuse (degrees or radians)

Explanation: The calculator computes both the cosine value and the corresponding angle in degrees.

3. Applications of Cosine

Details: Cosine is used in right triangle calculations, wave functions, circular motion, AC circuits, and vector decompositions.

4. Using the Calculator

Tips: Enter lengths of adjacent side and hypotenuse (must be positive numbers). The adjacent side cannot be longer than the hypotenuse in a right triangle.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of cosine values?
A: In right triangles, cosine values range from 0 to 1 (0° to 90° angles).

Q2: How is this different from sine?
A: Sine uses opposite/hypotenuse while cosine uses adjacent/hypotenuse.

Q3: What units should I use?
A: Any consistent length units (cm, m, inches, etc.) as long as both measurements use the same unit.

Q4: Can I use this for non-right triangles?
A: No, this formula is specific to right triangles. Use the Law of Cosines for other triangles.

Q5: What if my adjacent is longer than hypotenuse?
A: In a right triangle, this is impossible. Check your measurements.