Sine Calculator

Sine is a mathematical function that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. In simpler terms, sine is defined as the ratio of the length of the side opposite to a given angle to the length of the hypotenuse in a right triangle. It is denoted as sin(x), where x represents the angle.

The sine function takes an angle (in radians or degrees) as input and returns a value between -1 and 1. The value indicates the ratio between the vertical displacement and the hypotenuse length in the right triangle.

The sine function is widely used in various fields such as mathematics, physics, engineering, and computer science. It plays a fundamental role in trigonometry, waveforms, periodic functions, and many other applications involving angles and oscillatory phenomena.

The sine formula relates the angles and sides of a right triangle. In a right triangle, if we denote one of the acute angles as θ, the lengths of the sides opposite, adjacent, and hypotenuse as opposite side (opposite), adjacent side (adjacent), and hypotenuse (hypotenuse) respectively, then the sine formula is defined as:

sin(θ) = opposite / hypotenuse

Alternatively, we can use the Pythagorean theorem to express the sine formula as:

sin(θ) = sqrt(1 - cos^2(θ))

where cos(θ) denotes the cosine of the angle θ.

These formulas allow us to calculate the sine of an angle when we know the lengths of the sides of a right triangle, or vice versa, to find the length of a side when the angle and one side length are known. The sine formula is fundamental in trigonometry and has various applications in fields like geometry, physics, engineering, and wave analysis.