Trig, Coterminal angles... Which of the following are coterminal with -pi/4 ... (a) 7pi/4 (b)3pi/4 (c)-5pi/4) (d)-9pi/4 (e) pi/4

Question

anonymous · Answer

The answer is both (a) 7pi/4 and (b) -9pi/4

anonymous · Answer

I guess my question is... is there any short cut for knowing which ones to try first?

anonymous · Answer

Actually i am having trouble preforming the problem on my own and getting the right answer as well.

phi · Answer

2*pi is once around a circle.  If you start at -pi/4  and go 2*pi  or 4pi  or -2 pi you end up where you started.   I would make 2pi  8pi/4  (multiply top and bottom by 4)
now you can add 8pi/4 + -pi/4  to get 7 pi/4
there is not 16pi -pi = 15pi/4   

so try going backwards:  add -8pi/4 + -pi/4 = -9pi/4
if you go backwards twice:  -16pi/4 -pi/4 = -17pi/4  but that is not on your list