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. In the unit circle, it represents the x-coordinate of a point at a given angle.

2. How to Calculate cos(2)

The calculation is performed using the mathematical cosine function:

Where:

• 2 — Angle in radians (approximately 114.59 degrees)
• The function returns a unitless ratio between -1 and 1

Explanation: The cosine of 2 radians is calculated using the mathematical cosine function, which can be computed through Taylor series expansion or using built-in functions in programming languages.

3. Understanding the Result

Details: The result of cos(2) is approximately -0.416147 (unitless). This indicates that for an angle of 2 radians, the x-coordinate on the unit circle is negative, placing the angle in the second quadrant.

4. Practical Applications

Applications: The cosine function is widely used in physics, engineering, signal processing, and computer graphics. It's essential for analyzing periodic phenomena, wave functions, and rotational systems.

5. Frequently Asked Questions (FAQ)

Q1: Is the input in degrees or radians?
A: The calculation uses radians. To convert from degrees, multiply by π/180.

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

Q3: How accurate is this calculation?
A: The calculation uses PHP's built-in cos() function which provides high precision.

Q4: What does a negative result mean?
A: A negative result indicates the angle is in the second or third quadrant of the unit circle.

Q5: Can I calculate cosine for complex numbers?
A: This calculator handles real numbers only. Complex cosine requires additional mathematical operations.