Math Homework. Do It Faster, Learn It Better.


The sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.

sine = length of the opposite to the angle length of the hypotenuse abbreviated as “sin”.


In the triangle shown, sin A = 6 10 or 3 5 and sin B = 8 10 or 4 5 .

The sine ratio is the same regardless of the size of the right triangle. So, it is often easiest to consider a right triangle with a hypotenuse of length 1 .

The sine ratio can also be thought of as a function, which takes different values depending on the measure of the angle. You can measure an angle in degrees or  radians .

The reciprocal of the sine ratio is known as cosecant ratio of an angle, abbreviated as "cosec".

That is,

cosecant = length of the hypotenuse length of the leg opposite to the angle

In the above example, cosec A = 9 4 and cosec B = 9 7 .

See also: cosine and tangent .