If you have difficulty remembering the values of sine and cosine at the standard angles, make use of this diagram. The diagram is easier to remember than just a long list of values, and is in fact the diagram that defines the functions in the first place.
The standard angles are listed along the unit circle, going counterclockwise from 0 located on the positive part of the x-axis. The cosine function for a given angle is defined as the x-coordinate of the resulting point; the sine function is the y-coordinate.
Note that the diagram has many symmetries. Furthermore, the values of sine and cosine for each of the standard angles are always taken from a small collection of possible values...
First, note that for any multiple of pi/2, the values of sine and cosine are always either 0, 1, or -1. To remember which one, you need only remember where the angle in question is on the unit circle, and then remember that cosine is the x-coordinate, and sine is the y-coordinate.
For the other angles, the idea is similar. Knowing which quadrant the angle is in immediately reduces the possible answers to three; you then only need to remember which of the three angles in that quadrant it is to know which of the three possible answers is correct.
For example, we know that pi/6 is in the first quadrant, so sin(pi/6), the y-coordinate, can only be three possible things. Recalling further that pi/6 is the lowest (smallest y-coordinate) of the three standard angles in that quadrant, we can easily conclude that sin(pi/6) is 1/2, the lowest of the possible answers.
Using this method, you can recall the values of sine and cosine for all of the standard angles simply by remembering where those standard angles are on the diagram.
I hope you will find this helpful!