Sine and Cosine

Trigonometry is the study of the relationship between the angles and sides of triangles. The two most essential parts of trig are the functions sine and cosine. Both take an angle, and return a number. The way they work is really quite simple.

A diagram showing sine (abbreviated sin) and cosine (cos)

To find the sine of the angle θ, draw a circle with radius 1 on a graph, and put the circle's center at the origin of a graph. Find a point on the edge of the circle. The point makes an angle with the center of the circle; make sure that the angle is θ. Sine of θ is the point's y-coordinate. Cosine is the point's x-coordinate. (See the picture to the right.)

Sine and cosine are very useful for calculating heights and distances. For example, let's say somebody needs to know the height of a sky scraper, but isn't able to measure it physically with a tape. If he walks a certain distance away from it, and looks at the angle it subtends in the sky, he can use trigonometry to figure out its height.

But that's not all. If you graph the sine function, you get a cool wavy line the shape of a ripple in water. That curve is called a "sine wave". The same curve is also the building block for the shapes of sound waves. Who said math had to be boring? Not I.