In a right triangle, the sine of an angle is the length of the opposite side divided by the hypotenuse. For a 30-degree angle, sin 30° = 0.5. The function extends to all angles through the unit circle.

Sine is periodic, repeating every 360 degrees or 2π radians. Its graph is a smooth wave. Along with cosine and tangent, it is one of the basic trigonometric functions. The law of sines relates sides and angles in any triangle.

Sine describes wave motion, oscillations, and rotations. It appears in sound, light, alternating current, and quantum mechanics. Fourier analysis decomposes signals into sine and cosine components. The function is essential in physics, engineering, and signal processing.

• Ratio of opposite side to hypotenuse
• Periodic with period 2π
• Graph is a smooth wave
• Used in waves, oscillations, and Fourier analysis