Please help me with this graphing problem. Pictures are included. Please explain how you got your answer, it would mean so much!

Question

Please help me with this graphing problem.  Pictures are included.  Please explain how you got your answer, it would mean so much!

anonymous · Answer

attachment

anonymous · Answer

above is the question in picture form.

anonymous · Answer

And here are the options. They are in order from A-D.

anonymous · Answer

You have to evaluate y = cot (@/3) for a variety of values of @ and then
plot them. Start with @=0 to eliminate one or more of the options.
Since cot(@) = 1/tan(@) and tan(0)=0, you can eliminate A and B.

anonymous · Answer

Okay, great, then is it C?

anonymous · Answer

@douglaswinslowcooper Was I on the right path with my calculations?  Is it C?

anonymous · Answer

Did you calculate that or make an educated guess?

anonymous · Answer

Tried my best to calculate it.

anonymous · Answer

Should not have gotten a negative value at large @.
 cot(@) = 1/tan(@). Since tan(0) = 0, and
1/0 is infinite, we can rule out A and B. 

For @=2 pi, @/3 = (2/3) pi = 240o for
which tan(240)= 1.73 and cot(240)= 1/1.73 = 0.58. C shows a value <0 at
@= 2 pi. Rule it out , too. Leaves? D

anonymous · Answer

@douglaswinslowcooper  Thank you!  Okay, I think I got it now.  Best Answer for you!  But one quick question, did you use a calculator for this? Just wondering, really.