1. What is the Cosine Function?

The cosine function is a fundamental trigonometric function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. It's periodic with a period of 2π radians (360 degrees) and ranges between -1 and 1.

2. How Does the Calculator Work?

The calculator uses the mathematical cosine function:

Where:

• \( x \) — Angle in radians or degrees
• Adjacent Side — Side next to the angle in a right triangle
• Hypotenuse — Longest side of a right triangle

Explanation: The calculator computes the cosine using PHP's built-in cos() function, with optional degree-to-radian conversion.

3. Importance of Cosine Calculation

Details: Cosine is essential in mathematics, physics, engineering, and computer graphics for wave analysis, rotations, and periodic phenomena.

4. Using the Calculator

Tips: Enter any angle value and select whether it's in radians or degrees. The calculator will return the cosine value between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is cos(1)?
A: cos(1 radian) ≈ 0.5403. This is the default calculation when no input is provided.

Q2: What are the maximum and minimum values of cosine?
A: The cosine function always returns values between -1 and 1, inclusive.

Q3: How is cosine different from sine?
A: Cosine gives the ratio of adjacent/hypotenuse, while sine gives opposite/hypotenuse. They're phase-shifted by π/2 radians (90 degrees).

Q4: Can I calculate cosine for very large angles?
A: Yes, the calculator handles angles of any size by automatically reducing them to their equivalent within one period (2π radians or 360 degrees).

Q5: What's the precision of the calculation?
A: Results are accurate to 4 decimal places, matching typical trigonometric tables.