How do you memorize the Unit Circle?

Question

The unit circle can be daunting. It is necessary in all higher math classes and I am positive you will have a quiz or test on filling in the X and Y coordinates for each of the angles in the Unit Circle. I have an easy way to ace your quiz or test in filling in the Unit Circle.

Answer 1

I use the following "unforgettable chart" from my high school trig teacher ("Boston" Bob Connolly):

n 0 1 2 3 4 n is the column which numbers the angles in Q1

θ 0 π/6 π/4 π/3 π/2 θ is the angle in radians in Q1

sinθ=√n/2 0 1/2 √2/2 √3/2 1 √n/2 generates the exact values of sinθ

cosθ 1 √3/2 √2/2 1/2 0 cosθ is sinθ backwards (the complement)

tanθ 0 1/√3 1 √3 ∞ tanθ = sinθ/cosθ

The key is plugging in each column number n in sequence, noting for n=4 that √4/2 = 2/2 = 1.

Just remember the formula √n/2 and you can construct sinθ and cosθ whenever you forget them.

That gets you Quadrant 1 and you get sinθ and cosθ in the other quadrants by using the appropriate sign.

Answer 2

Know SOHCAHTOA, know your 30-60-90 triangles, 45-45-90 degree triangles; know that there are 2 pi radians in a circle, and thus what pi/2, pi/3, pi/4 and pi/6 mean, draw little triangles on a coordinate plane with reference angles on the x- axis then you can construct that circle that students are often asked to memorize. But there is a reason you are being asked to memorize it, THE INFORMATION THAT IT CONTAINS WILL BE NEED AS YOU PROCEED IN HIGHER MATH. Draw pictures of those triangles, understand when certain triangles drawn on the plane generate positive and negative trig ratios and be confident that you can figure sin, cos, and tan of any of 30-45-60-90 reference angles in any quadrant and you'll be good.