What is the period of a sine cosine curve?
So, what is the formula for the period?
If you look at the prior 3 pictures, you might notice a pattern emerge.. The period has a relationship to the value before the $$ \theta $$
This pattern is probably easiest to see if we make a table.
Equation  Period  Picture 

$$ y = sin ( \color{red}{1}\theta )$$  $$ \color{red}{2} \pi $$  
$$ y = sin ( \color{red}{2}\theta )$$  $$ \color{red}{ 1 }\pi $$  
$$ y = sin ( \color{red}{\frac{1}{2}}\theta )$$  $$ \color{red}{ 4\pi } $$  
$$ y = sin ( \color{red}{4}\theta )$$  $$ \color{red}{ \frac{1}{2} \pi } $$ 
Can you guess the general formula?
As you might have noticed there is a relationship between the coefficient in front of $$ \theta$$ and the period. In the general formula, this coefficient is typically labelled as 'a'.
The general formula for $$ sin( \color{red}{a} \theta )$$ or $$ cos( \color{red}{a} \theta )$$ is
$ period = \frac{2 \pi}{ \color{red}{a}} $
Practice Problems
To solve these problems, just start at the xaxis and look for the first time that the graph returns to that 'height.' So, in this case, we're looking for the time when the graph returns to the .5 value which is at $$ 2 \pi$$.
Remember: Find the height of the graph at the xaxis and then look for the first time that the graph returns to that height. In this case, the answer is $$ \pi $$ or just $$ \pi $$.
Graphs generated by http://www.metacalculator.com
Remember: The formula for the period only cares about the coefficient, $$ \color{red}{a} $$ in front of the x. The formula for the period is the coefficient is 1 as you can see by the 'hidden' 1:
$$ 2sin( \color{red}{1}x) $$
$ period = \frac{2 \pi}{ \color{red}{a}} \\ period = \frac{2 \pi}{1} \\ period = 2 \pi $
Remember: The formula for the period only cares about the coefficient, $$ \color{red}{a} $$ in front of the x. The formula for the period is the coefficient is 8 :
$$ 7 cos ( \color{red}{8}x) $$
$ period = \frac{2 \pi}{ \color{red}{a}} \\ period = \frac{2 \pi}{ 8} \\ period = \frac{ \pi}{4} $
So, the big question here is: what do we do about the negative sign? Well, the answer is, we do not worry about the negative sign. Period tells us how long something is, and it must be a positive number.
$$ 3cos( \color{red}{2}x) $$
$ period = \frac{2 \pi}{ \color{red}{a}} \\ period = \frac{2 \pi}{2} \\ period = \pi $
Demonstration
of Period of sine Graph & Connection Unit Circle

Further Reading:
 Unit Circle Game Free online game on all things about the unit circle
 Unit Circle Printables Images of blank unit circles and blank unit circles with the answers filled in
 Worksheet on graphing sine and cosine
 graph and formula of unit circle formula for period of sine  demonstration of period of sine