What does it mean for angles to be coterminal? Can I have an example?

Answer 1

Angles consist of two rays exiting a common vertex. In trig, we place that vertex at the origin and the right-side ray (called the initial side) is placed on the positive x-axis. The left-side ray is called the "terminal side" of the angle. Like this:

So, think of the initial side as fixed and you rotate the terminal side around in the counterclockwise direction to any angle you desire. Since you can rotate the terminal side around more than one revolution, it is possible that one angle rotated a small amount, say 30°, and another angle rotated a little more than 1 revolution, say 390°, end up with their terminal sides on top of one another. This is said to be co-terminal.