1. What is 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 360° (2π radians) and ranges between -1 and 1.

2. How Does the Calculator Work?

The calculator computes the cosine using the mathematical function:

Where:

• \( \theta \) — Angle in degrees

Explanation: The calculator converts the angle from degrees to radians (since PHP's cos() function uses radians) and then calculates the cosine value.

3. Importance of Cosine Calculation

Details: Cosine is essential in mathematics, physics, engineering, and computer graphics. It's used in wave analysis, circular motion, signal processing, and vector calculations.

4. Using the Calculator

Tips: Enter any angle in degrees (positive or negative). The calculator will return a value between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of cosine values?
A: The cosine function always returns values between -1 and 1, inclusive.

Q2: How is cosine different from sine?
A: Cosine represents the x-coordinate (adjacent/hypotenuse) while sine represents the y-coordinate (opposite/hypotenuse) in the unit circle.

Q3: What are some special cosine values?
A: cos(0°) = 1, cos(90°) = 0, cos(180°) = -1, cos(270°) = 0, cos(360°) = 1.

Q4: Can cosine be greater than 1 or less than -1?
A: No, for real angles, cosine values are always in the range [-1, 1].

Q5: How is cosine used in real-world applications?
A: It's used in AC circuit analysis, sound waves, light waves, mechanical vibrations, and GPS calculations.