# Cosine and the graph of cos(x)

Note by rory.examtime, updated more than 1 year ago
 Created by rory.examtime over 7 years ago
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### Description

This note gives a definiton of cosine of an angle, and explains the shape of the y = cos(x) graph

## Resource summary

### Page 1

In a right-angled triangle, the cosine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Cos(X) = A                H

For example, in this triangle:

the cosine of angle A (CosA) is 0.6, because the ratio of the opposite side (3) to the hypotenuse (5) is 3/5.

Graph of cos(x):

-Note that x, the angle, is in radians, not degrees.

- Similarly to sin(x), this graph is often referred to as a wave, and has a period of 2π (after every 2π radians, the graph repeats it self)

- In fact, the graph of cos(x) is identical in shape to the sin(x) graph, just out of phase by π/2.

- This means that sin(x) = cos(x+π/2).

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