# How do you determine the period for y = cos (2pix)?

Apr 27, 2015

You can use the $2 \pi$ in front of $x$ in the argument of $\cos$.
Calling this number $k$ you have that:
$k = \frac{2 \pi}{p e r i o d}$
So in your case you have $p e r i o d = 1$
graph{cos(2pix) [-2.433, 2.435, -1.215, 1.217]}

Apr 27, 2015

Another way to think about it:

$\cos \left(\theta\right)$ has a period of $2 \pi$
You can think of this as meaning that the values
$\text{ from " cos(0) " to } \cos \left(2 \pi\right)$
make up one period.

So the question is what values of $x$
would cause $\cos \left(2 \pi \cdot x\right)$ to take on the range
$\cos \left(0\right) \text{ to } \cos \left(2 \pi\right)$

The answer is obviously $x = 0 \text{ to } 1$
So the period is $1$