1. What is the Sine Function?

The sine function is a fundamental trigonometric function that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of 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 sine function:

Where:

• \( \theta \) — Angle in radians or degrees
• opposite — Length of side opposite to angle
• hypotenuse — Length of the hypotenuse

Explanation: The calculator converts degrees to radians if needed, then computes the sine using PHP's built-in sin() function.

3. Importance of Sine Calculation

Details: Sine calculations are essential in mathematics, physics, engineering, signal processing, and many other fields. They're used to model periodic phenomena, analyze waveforms, and solve problems involving right triangles.

4. Using the Calculator

Tips: Enter the angle value and select whether it's in radians or degrees. The default value is 1 (radian). The calculator will compute sin(1) or sin of your specified angle.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radians and degrees?
A: Radians and degrees are two different units for measuring angles. 360 degrees equals 2π radians. Radians are often preferred in mathematical calculations.

Q2: What is sin(1) in radians?
A: sin(1) ≈ 0.841471 when 1 is in radians.

Q3: What is sin(1) in degrees?
A: sin(1°) ≈ 0.017452 when 1 is in degrees.

Q4: What are the applications of sine function?
A: Sine functions are used in physics for wave motion, in engineering for signal processing, in computer graphics for animations, and in navigation for calculating distances.

Q5: How accurate is this calculator?
A: The calculator uses PHP's built-in sin() function which provides high precision results (typically to about 14 decimal places).