## sine

### ratio of the opposite side to the hypotenuse of a right-angled triangle

Sine is one of the trigonometric functions that relates the ratios of the sides of a right triangle. Specifically, the sine of an angle in a right triangle is equal to the length of the opposite side divided by the length of the hypotenuse. The sine function is denoted by the abbreviation sin and takes an angle as its input.

For example, if we have a right triangle with an acute angle of θ, where the opposite side is 3 units long and the hypotenuse is 5 units long, we can find the sine of θ using the following formula:

sinθ = opposite/hypotenuse

sinθ = 3/5

In this case, the sine of θ is equal to 0.6.

The sine function has many important properties and applications in mathematics, physics, and engineering. It is periodic, meaning that it repeats itself after every 360 degrees or 2π radians. The sine function is also symmetric about the origin, so sin(-θ) = -sin(θ) for all angles θ.

In addition, the sine function is used to describe many types of wave phenomena, including sound waves and electromagnetic radiation. It is also used in signal processing and other areas of engineering where the analysis of periodic signals is important.

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