Sine function, sin(x)

Sine definition

In a right triangle ABC the sine of α, sin(α) is defined as the ratio betwween the side opposite to angle α and the side opposite to the right angle (hypotenuse):

sin α = a / c


a = 5″
c = 10″
sin α = a / c = 5 / 10 = 0.5

Graph of sine


Sine rules

Inverse sine function

The arcsine of x is defined as the inverse sine function of x when -1 ≤ ≤ 1.

When the sine of y is equal to x:

sin y = x

Then the arcsine of x is equal to the inverse sine function of x, which is equal to y:


arcsin x = sin-1(x) = y

Sine table