1. What is the Sine Function?

The sine function is a fundamental trigonometric function that describes the ratio of the length of the opposite side to the hypotenuse in a right-angled triangle. It's periodic with a period of 2π radians (360 degrees) and oscillates between -1 and 1.

2. How Does the Calculator Work?

The calculator computes the sine function:

Where:

• \( x \) — Angle in radians or degrees

Explanation: The function calculates the trigonometric sine of an angle. If degrees are selected, the angle is first converted to radians before calculation.

3. Importance of Sine Function

Details: The sine function is essential in mathematics, physics, engineering, and signal processing. It describes periodic phenomena like sound waves, light waves, and alternating current.

4. Using the Calculator

Tips: Enter the angle value and select whether it's in degrees or radians. The calculator will compute the sine of the angle.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the difference between degrees and radians?
A: Degrees divide a circle into 360 parts, while radians use the radius as a unit (2π radians = 360 degrees).

Q3: What are some practical applications of sine?
A: Used in AC circuit analysis, sound engineering, signal processing, and modeling periodic phenomena.

Q4: What's the relationship between sine and cosine?
A: The cosine function is just the sine function phase-shifted by π/2 radians (90 degrees).

Q5: How accurate is this calculation?
A: The calculation uses PHP's built-in sin() function which is highly accurate for most practical purposes.