The normal period of cos is 360 degree (or radians). The 1/2 in front of theta means that the period will be twice a long: 720 degrees (or radians).
There is no vertical or horizontal shift.
Here are the graphs of both y = cos(theta) and your equation. I'll leave it up to you to figure out which is which. (Note: I do not how to get Algebra.com's graphing software to use degrees. So the graph below is in radians. You will have to convert the radians to degrees using the fact that radians equals 360 degrees.)