Question

Part A: In your own words, describe the steps that are necessary to determine whether angles are coterminal.

Part B: Explain why coterminal angles have a difference that is a multiple of 360° degrees, such as 720° or 1080°.

Part C: Find three angles that are coterminal with an angle measuring 75°. Show all work.

Answer 1

Part A:

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom

Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.

Explanation: