What is the ratio for sine?

The sine ratio, often denoted as sin, is a trigonometric function that relates the length of the opposite side of a right triangle to the length of the hypotenuse. In other words, it is the ratio of the length of the side opposite a given angle to the length of the hypotenuse.

Mathematically, the sine of an angle θ in a right triangle is given by the following formula:

sin(θ) = opposite side / hypotenuse

The sine function is periodic with a period of 360 degrees or 2π radians, meaning that the sine of an angle repeats at regular intervals. On the unit circle, the sine function equals the y-coordinate of a point on the circumference of the circle at a given angle.

The values of the sine function range from -1 to 1, with a maximum value of 1 when the angle is 90 degrees or π/2 radians. The sine function is also an odd function, meaning that sin(-θ) = -sin(θ) for all angles θ.

The sine ratio is used in various fields, including mathematics, physics, engineering, and navigation, to calculate distances, angles, velocities, and more. It is a fundamental trigonometric function and is commonly used in solving right triangle problems and analyzing periodic phenomena.