# Trigonometric Functions as Projections

## The period of the cosine function

Remember there is no difference between the position of a point
*P* on the unit circle for an angle \(\theta\) and the position
for angle \(\theta + n \times 360^\circ\), where *n* is a
positive or negative integer. And if point *P* is the same,
then the projection onto the *x-*axis must also be the
same. From this we can conclude:

\[\cos(\theta)=\cos(\theta + n\times 360)\]
The result of this is that, like the sine function, \(\cos(\theta)\)
is a *periodic function*. The function repeats itself every 360
degrees, as shown in the interactive below.

## Exercises

- What is the
*domain* of the cosine function? (That is, for \(y=\cos(\theta)\) what are
the minimum and maximum values \(\theta\) can take?)
- Calculate \(\cos(360\,000\,036^\circ)-\cos(-324^\circ)\).
- For what values of \(\theta\) does \(\cos(\theta)\)
- reach its maximum value?
- reach its minimum value?
- intersect
the horizontal axis?