Cosine: the Point's x

The other coordinate of the point on the unit circle is cos(theta): how far the point is to the right of the centre, negative when it is to the left. At 0° the point is at (1, 0), so the cosine starts at 1. At 90° the point is straight up, x = 0. At 180° it is at the far left, x = −1. At 270° x is 0 again, and at 360° it is back to 1.

The point at 60°: its x coordinate is 1/2.

Mirror images do the rest. The point at 60° has x = 1/2, so cos(60°) = 1/2. The point at 300° is its mirror image below the x axis, with the same x: cos(300°) = 1/2. A mirror image across the y axis keeps the height and changes the sign of x.