Draw the angle given in degrees on the unit circle where 0° corresponds to the positive portion of the horizontal axis: 300°.

Question

Draw the angle given in degrees on the unit circle where 0° corresponds to the positive portion of the horizontal axis: 300°.

Answer 1

On the unit circle, it is common to refer to the "positive horizontal axis/positive x-direction" as 0^o  and to refer to a positive angle as a counterclockwise "spin" - this will make sense in a moment. The two axes form a "+" sign. There are four arms - one pointing up, one pointing down, one pointing left, and the last pointing right. The one pointing right is the positive horizontal axis (the one pointing left is negative). 

Now imagine that you are drawing a circle with a compass. You put the pin in the center, and set the pencil so that it makes a circle of radius 1 (inch, cm, mm, whatever you choose). You spin the compass counterclockwise (because of the positive angle), and what you have created is the unit circle.

To create this circle, you have spun the compass a full 360 degrees. Where did you start? On the "positive portion of the horizontal axis" - the right arm of the + sign. If 360 takes you around the entire compass, then it takes you 180 to get halfway around, or facing directly opposite the direction you were before, on the negative portion of the horizontal axis (the left arm). Spinning another 90 degrees, for a total of 270, gets you to the bottom arm. Thus, you need only spin another 30 to get to 300 degrees. If you start on the bottom arm and spin 30 degrees counterclockwise, you will find the appropriate spot - 1/3 of the way along the arc between the bottom arm and the right arm.