Right triangle and cosine

A **cosine**, like a sine, is a mathematical way of thinking about a kind of movement that happens in nature. A cosine is really just a rephrasing of the same information we already had for calculating the sine function.

One way to describe these changes is with the sine function. Choose one of the two angles – A in this drawing – and divide the length of the side opposite that angle by the length of the hypotenuse. As the angle gets bigger, the opposite side will get longer. The sine will get bigger. But a second way is with the cosine function. Instead of dividing the opposite side by the hypotenuse, the cosine divides the adjacent side by the hypotenuse. As with sines, if you change the lengths of the sides of the triangle, the cosine changes along with the sine.

The cosine wave and the sine wave for the same natural phenomenon go up and down by the same amount, but out of phase: the cosine reaches the bottom of the wave when the sine is at zero, and the sine reaches the bottom of the wave when the cosine is at zero. Cosines are useful mainly because they let people work out how far away something is just by knowing the angle near them and the length of the hypotenuse, or work out the size of an angle by knowing the length of two sides.

## Learn by doing: have two people each hold one end of a rope. Wiggle the rope between you to see a sine wave.

More about Sines

More about Trigonometry

## Bibliography and further reading about trigonometry:

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