In the video below, you will see how to memorize the value of the trig functions for all the common angles, including the quadrantal angles like 0° and 180°. This is based on this huge table of values for the trig functions (you can find a blank copy there too). For the process we will look at, memorize may be the wrong word since it is more about understanding how the values work with each other. Even so, after some practice, you won’t need the table to be able to answer the question “what is \(\sin\left(\dfrac{\pi}{3}\right)\)” because you will have the idea of the table in your head!

You may notice that this is, in a way, very similar to learning/memorizing the unit circle. Even so, you would still use the unit circle after memorizing this. For example, if you wanted to know the \(\sin\left(\dfrac{2\pi}{3}\right)\), you would still use the value you have in this table as a reference angle and then the sign would come from the quadrant. The unit circle already has that “built in”, but has more angles laid out than this table.