What is the Unit Circle anyway? We begin with a circle of radius 1 (hence, unit circle) graphed on the Cartesian axes.

Circle with radius of 1.

Then we divide the circle up into specific sections.

These sections correspond to special angles.

Let’s take it one part at a time…

We need to establish some reference points.

Now we’re going to start dividing the circle up Now we’re going to start dividing the circle up. We begin by dividing by 4’s.

Let’s divide by 3’s this time.

And now by 6’s.

This is what it looks like all together.

So now we have all these special angles So now we have all these special angles. You need to be able to locate them. Don’t worry. It’s easy.

Let’s practice.

This is all you get…

There are patterns; look for them! So now that we have all the special angles and you can identify where they are located. We can consider the trig values for each of these angles. There are patterns; look for them!

−𝟏 𝟐 , 𝟑 𝟐 𝟏 𝟐 , 𝟑 𝟐 − 𝟐 𝟐 , 𝟐 𝟐 𝟐 𝟐 , 𝟐 𝟐 𝟎,𝟏 − 𝟑 𝟐 , 𝟏 𝟐 𝟑 𝟐 , 𝟏 𝟐 −𝟏,𝟎 𝟏,𝟎 − 𝟑 𝟐 , −𝟏 𝟐 𝟑 𝟐 , −𝟏 𝟐 − 𝟐 𝟐 , − 𝟐 𝟐 𝟐 𝟐 , − 𝟐 𝟐 𝟎,−𝟏 −𝟏 𝟐 , − 𝟑 𝟐 𝟏 𝟐 , − 𝟑 𝟐

All the special angles with the same denominator have the same trig values, except for the sign.

All other angles have the same trig values. This means that all you have to memorize are the values for the angles in the first quadrant. All other angles have the same trig values. Identify where they are on the circle and you know the signs.

Let me show what I mean…

Unit Circle

Different ways to memorize the values. There are three. Do not take notes yet. Wait until you pick a method you like.

My Method

This is what you have to remember.

Meliha’s Method

This is what you have to remember.

Rex’s Method

This is what you have to remember. Number: 3, 2, 1, 3, 2, 1 Take the square root of everything. This is what you have to remember. Divide everything by 2. __ 1 __ 3 2 2 __ 2 __ 2 2 2 __ 3 __ 1 2 2