Find ALL the coterminal angles to -160 degrees

Question

Please answer and show work!

Answer 1

1. coterminal angles are angles with the same terminal side
2. the angles always move counterclockwise or clockwise from the +x axis
3. a positive coterminal angle would be= 360-160= 200 degrees
4. there is no range so there can be an infinite number of rotations and therefore infinite coterminal angles
5. all positive coterminal angles= 200+ n*360 degrees
6. n=0,1,2,3... and is represented by a full rotation
7. negative coterminals= -160 - n*360
8. in general:
9. positive terminals= angle + n*360
10. negative coterminals= angle - n*360

Answer:

200+ n*360 ; -160 - n*360 degrees

Answer 2

Since we can't list all the co-terminal angles ( because there is an infinite amount!) we will write an expression that will represent all of them. Since any full rotation from the original angle of -160 degrees ( which is the same as a 200 degree angle) will line up with the original angle, we can add or subtract any multiple of 360 degrees to the original angle to represent all the other angles that would also be positioned exactly the same way. If we let "n" be the number of full rotations from the original angle, the expression would look like this:

-160 +/- 360n ( or, we could also write it as 200 +/- 360n ) degrees). The +/- sign allows us to rotate either in the clockwise or the counterclockwise direction from the original angle.

Answer 3

-160°=200°

If you add or subtract 360°; it'll be the same.