Unit Circle

In the Unit Circle, there are three special right triangles.  As you can see on the right, the triangles are drawn in the circle. The hypotenuse of each triangle will be 1 because the radius all around the circle is 1.  "X" would be considered the adjacent side and "y" would be considered the opposite side (this is going back to geometry).  We will be looking at the triangles on the first quadrant to make it simpler.  We know one point will be (0, 0) because it is in the middle of the graph.

The green triangle is a 30, 60, 90 triangle. To find the coordinates of the triangle, we look at the points it is touching on the circle. For the green triangle, the point it hits is (rad3/2, 1/2). So the coordinate of "x" would be (rad3/2, 0) because the it is lying on the x-axis. The coordinate of the "y" would be (rad3/2, 1/2).

The red triangle is a 45, 45, 90 triangle. We find the coordinates the same way. The point corresponding to this triangle is (rad2/2, rad2/2).  So we know our "x" point would be rad2/2, 0) and our "y" point would be (rad2/2, rad2/2).

The blue triangle is a 30,60, 90 triangle. The point corresponding to this triangle is (1/2, rad3/2). From there we can find our points. "X" would be (1/2, 0) and "y" would be (1/2, rad3/2).