Sine of Angles

Sine of Angles

The Sine and Cosine are the two most important tools we use to measure triangles in Mathematics.

The sine ("sin") and cosine ("cos") are the two most prominent trigonometric functions. All other trig functions can be expressed in terms of them. In fact, the sine and cosine functions are closely related and can be expressed in terms of each other.

This means that almost everything we do in trigonometry starts with these two partners, and they work together like twins.

What Sine means

The Sine rule helps us see how the corner of a triangle and the sides of that triangle work together.

The sine definition basically says that, on a right triangle, the following measurements are related:

The measurement of one of the non-right angles (theta)

The length of the side opposite to that angle

The length of the triangle’s hypotenuse

To use this rule, you must look at one small angle, the side facing it, and the longest side of the triangle.

The Sine Formula

This is the formula we use to calculate the sine of any angle.

sin theta = opposite/hypotenuse

It means you should divide the length of the side facing the angle by the longest side of the triangle.

If you press the sine of an angle on your calculator, the answer will be the same as when you divide the opposite side by the longest side.

If we evaluate the sine of the angle theta, we will get the exact same value as if we divided the length of the side opposite to that angle by the length of the triangle’s hypotenuse.

So, the ratio you get from the sides is always the same as the sine of that angle.