Junior Cert and Leaving Cert students do not need to memorise many points on the unit circle because they are given on page 13 of the Formulae and Tables approved for use in the state examinations. However, if you can do so easily it is no harm, and can be useful in that it will save you time looking it up in the booklet. Here are the links to two useful videos on the unit circle.
The first explains how you can use the palm of your left hand as a memory aid to remember the values of the coordinates of various standard angles.
The second gives a more detailed description to enable understanding.
If you have problems with the unit circle have a look at them.