Sine

Sine is a fundamental concept in trigonometry, a branch of mathematics that studies the relationships between the angles and sides of triangles. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Definition

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. This is often abbreviated as "SOH" in the mnemonic "SOHCAHTOA" used to remember the definitions of the sine, cosine, and tangent functions.

Properties

The sine function has several important properties. It is a periodic function, meaning it repeats its values in regular intervals. The period of the sine function is 2π radians or 360 degrees. The sine function is also an odd function, which means that for any angle θ, sin(-θ) = -sin(θ).

Applications

The sine function is used in a wide variety of fields, including physics, engineering, computer science, and statistics. In physics, it is used to model periodic phenomena such as sound and light waves. In engineering, it is used in signal processing and control systems. In computer science, it is used in graphics and animation. In statistics, it is used in the analysis of periodic data.

See also

• Cosine
• Tangent
• Unit circle
• Trigonometric functions
• Trigonometry