The only way to memorize the unit circle is to solve as many math trigonometry related problems that use the values of the unit circle as you possibly can. That way it becomes second nature. It takes time and practice. It's not impossible.

Or maybe nag your teacher to let the class use it on the tests. Or! Or... print out a unit circle and put it under your pillow before you go to sleep. Don't fold the paper because that won't let you absorb and remember the numbers. Hopefully, through osmosis while sleeping at night you will have all the needed values printed in your brain when you wake up in the morning.

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