Answer:
Step-by-step explanation:
Left hand column
-780 works. The arm swings around the origin like a clock twice which makes - 720. You have - 60 left over so that one works.
- 420 works. The clock hand swings around the origin once clockwise. The arm still has -60 to go . - 60 is what you want.
300 will wind up in the same place as - 60. Both are in the 4th quad in the same place.
660 will do the same thing as 300. 660 - 360 = 300. Both 300 and -60 have same terminal arm.
-1020 looks like it works, but it does not. The clock hand swings around the origin twice. That's - 720. You still have - 300 to go. That puts you in the 1st quadrant not the 4th.
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Right hand column
You have to be careful with this one. The reasoning is just slightly different.
145 degrees is in the second quadrant. If you have - 215, the arm will wind up in the same place as 145 (in the second quadrant). What you are looking for is something that is either 145 or - 215
-575 = one revolution around (360) with a remainder of -215 so this one works.
-215 works. See introductory statement for this problem.
505 works. 505 - 360 = 145. The arm swings around the +x axis once and the remainder is 145.
865 works. The terminal arm swings around the + axis twice and gives 865 - 2*360 = 865 - 720 = 145.
