To find the value of one of the 6 trig functions at any unit circle angle, you need to Determine 1: What is the reference angle? That is what angle does the given angle measure to the nearest x-axis angle? (0 or 180 or 360 or... degrees, or 0 or Pi or 2Pi... radians) The answer will always be a first quadrant angle. One useful fact about radians is that if your angle reduces to some /6, it has a Pi/6 reference angle. If it reduces to a /3, it is a Pi/3 reference ange. Same pattern for the /4 fractions and the /2 fractions. Determine 2: What is the value of the trig function at that reference angle? The following video can help a lot to determine the sine and cosine of those angles. With these two, you can easily find the other 4. Keep in mind that the values that are achieved are (cos, sin) values. They are always in that order.
Determine 3: In which quadrant is the original angle? This will determine the sign of the trig function at that angle. The following video is useful in understanding the "All Students Take Calculus" technique for determining sign.