Cos 2 in Calculator

Cosine Function:

\[ \cos(\theta) \]

Result:

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1. What is Cosine Function?

The cosine function is a fundamental trigonometric function that describes the ratio of the adjacent side to the hypotenuse in a right-angled triangle. It's periodic with a period of 2π and ranges between -1 and 1.

2. How Does the Calculator Work?

The calculator computes the cosine of 2 radians using PHP's built-in cos() function:

\[ \cos(2) \]

Where:

The input is 2 radians (approximately 114.59 degrees)
The calculation is performed using floating-point arithmetic
The result is rounded to 6 decimal places

3. Mathematical Explanation

Details: The cosine function can be represented as an infinite series:

\[ \cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots \]

For x = 2, this series converges to approximately -0.416147.

4. Using the Calculator

Tips: Simply click the "Calculate" button to compute cos(2). The result will be displayed in the output field.

5. Frequently Asked Questions (FAQ)

Q1: Is this in radians or degrees?
A: The calculation uses radians. 2 radians ≈ 114.59 degrees.

Q2: Why is the result negative?
A: Because 2 radians is in the second quadrant (between π/2 and π) where cosine values are negative.

Q3: How accurate is this calculation?
A: The PHP cos() function typically provides about 14 decimal digits of precision.

Q4: Can I calculate cosine of other values?
A: This specific calculator only computes cos(2). For other values, you would need a different calculator.

Q5: What are some practical applications of cosine?
A: Cosine is used in physics, engineering, signal processing, and many other fields involving periodic phenomena.