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The Cosine Graph

# The Cosine Graph

### The Cosine Graph

The Cosine graph also comes from trigonometry and is very similar to the Sine graph, but shifted left by 90 degrees.

The cosine graph is similar in shape to the Sine graph. Like the sine function, the cosine function also appears in the study of geometry in its connection with right angled triangles.

The Cosine measures the ratio between the adjacent side and the hypotenuse. It is defined as follows:

$cos(x)=\dfrac{adjacent}{hypotenuse}$

For $y = cos(x)$ between 0 and 360, the graph has a minimum when x is what value?

As with Sine graphs, Cosine graphs have more than one solution for each value of $cosx$. We can find the angle which corresponds to a $cosx$ value using the $cos^{-1}$ function.

For example, the corresponding angle for $cosx=1$ is:

$cos^{-1}(1)=0$

What is $cos^{-1}(0.5)$?

This is known as the principle value. We can then use the symmetry of the graph to find other points which also give this value.

For $y = cos x$ between 0 and 360, $cos66 = 0.4$. Another value of x that would give 0.4 is...