Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The question is, to generate a polar graph using a graphing utility, and to choose parameter interval so that the complete graph is generated.

$$r=\cos\frac{\theta}{5}$$

To find such an interval, we are looking for smallest number of complete revolutions until value of $r$ begins to repeat. Algebraically,this amounts to

$$\cos\frac{\theta}{5}=\cos\frac{\theta+2n\pi}{5}$$

For this equality to hold,$\frac{2n\pi}{5}$ must be an even multiple of $\pi$,the smallest n for which it occurs is $n=5$.Therefore, the graph will be traced completely in $5$ revolutions ($10\pi$).

But when I draw it the graph is completely traced in $5\pi$, where have I gone wrong?

share|improve this question
    
Try graphing $r=cos\theta$ by hand. It creates a circle between 0 and $\pi$. It re-traces the same circle between $\pi$ and $2\pi$. The same thing occurs in your graph. –  Paul Sundheim Aug 23 at 14:54
    
@PaulSundheim how is that same with this graph, this graph does not trace itself before $5\pi$, and i am getting $10\pi$. –  Ramanujan Aug 23 at 14:56
    
As you said, "the graph is completely traced in 5π" but now you say "this graph does not trace itself before 5π"? Which is the correct statement? –  Paul Sundheim Aug 23 at 14:59
    
I just traced it on a graphing calculator. Seemed to be complete in $5\pi$ and then repeated. –  paw88789 Aug 23 at 15:01
    
@PaulSundheim The graph is completely traced in 5pi means after that you are just tracing it again.I know 5pi is correct, do you mind telling where is the computation wrong? –  Ramanujan Aug 23 at 15:04

2 Answers 2

up vote 3 down vote accepted

$r(5\pi+t)=\cos(\pi+\frac{t}5)=-\cos(\frac{t}{5})=-r(t)$. Also the angle at $5\pi+t$ points in the opposite direction of the angle at $t$. Hence you get repetition.

share|improve this answer
    
$r(5\pi+t)=$?? what do you mean. –  Ramanujan Aug 23 at 15:13
    
He means $r$ evaluated at $5\pi+t$ –  Paul Sundheim Aug 23 at 15:15
    
got it thanks for the help. –  Ramanujan Aug 23 at 15:18
    
@Paul S. Yes. Thanks. –  paw88789 Aug 23 at 15:30

Since the question has been already answered, I post here a visual answer that I hope may help you to understand the problem better:

enter image description here

Cheers!

share|improve this answer
    
very helpful and cool, which utility is this. –  Ramanujan Aug 23 at 15:26
    
Hi @Shobhit. This was entirely done with Matlab. –  Dmoreno Aug 23 at 15:26
    
thank you again its cool –  Ramanujan Aug 23 at 15:28
    
You're welcome mate. –  Dmoreno Aug 23 at 15:31

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.