Rembering the Unit Circle?

Question

I have a trig. final coming up and i need to know the unit circle are there any good ways for remembering the whole circle

Answer 1

I agree with sazimme. Memorize the first quadrant only.

Draw the circle first, and label the three key angles:

π/6 = 30° = (√3/2, 1/2), tan = y / x = √3/3
π/4 = 45° = (√2/2, √2/2), tan = y / x = 1
π/3 = 60° = (1/2, √3/2), tan = y / x = √3

Then label the same angles in each quadrant the very same way, without worrying about signs.

Then either use Alabama State Teachers College (All are positive in quadrant 1, Sin is positive in 2, Tan in 3, Cos in 4)...or just remember that:

cosine has the same sign as x
sine has the same sign as y
tangent has the same sign as y/x

The angles that are multiples of 90° are easy:

0 = 0° = (1, 0), tan = y / x = 0
π/2 = 90° = (0, 1), tan = y / x = infinity
π = 180° = (-1, 0), tan = y / x = 0
3π/2 = 270° = (0, -1), tan = y / x = -infinity

Answer 2

Just practice. Really you only need to know one quadrant because everything is symmetric. Once you get to your test, immediately draw the circle on your paper before doing any work so you won't worry about it halfway through the test. These are the "tricks" I used in high school.

Answer 3

If you look elsewhere in these questions, someone asked for any memory tricks to use in precalculus. I wrote out a long explanation about how to memorize the unit circle values. If you look for precalc or precalculus in a question, it is a question asking for memory tricks (he wanted things like SOHCAHTOA).