March 21st, 2019, 09:35 AM  #1 
Newbie Joined: Oct 2018 From: Indoors Posts: 12 Thanks: 0  Polar gaphs
With x as θ, "Show by hand that the equations r = 1+sin(x) and r = sin(x)1 have the same graph." The solution says: r = 1+sin(x) r = 1+sin(x+pi) r = 1+sin(pi+x) r = 1sin(x) r = sin(x)1 I have no idea what theorem or test was used to justify that substitution. I was thinking that since the identitical graphs are symmetric with respect to the 1/2 pi axis, I should perhaps test the first equation for such symmetry. Thus, with r = 1+sin(x) we replace (r,x) by (r,pix) and we get r = 1+sin(pix) and an equivalent equation of r = 1+sin(x) is the result. Whereas if in r = 1+sin(x) we replace (r,x) by (r,x) r = 1+sin(x) r = 1sin(x) r = sin(x)1, we don't get an equivalent equation but the second equation is obtained nonetheless. Have I shown, in this way, that the two equations have the same graph. P.S. Sorry for the use of x instead of θ. Last edited by TheReluctantMathMan; March 21st, 2019 at 09:43 AM. 
March 21st, 2019, 10:15 AM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 647 Thanks: 94 
Yes you must use one of the trigonometric reduction formula. And it depends on what you mean with “same graph”. Example : same graph but in different plane . In this case consider translation of graph . $\displaystyle y=f(x)$ is the same graph of $\displaystyle f(x) +c$ . $\displaystyle f(x)=sin(x)$ and $\displaystyle c=\pm 1$ . Last edited by idontknow; March 21st, 2019 at 11:10 AM. 
March 22nd, 2019, 09:00 AM  #3  
Newbie Joined: Oct 2018 From: Indoors Posts: 12 Thanks: 0  Quote:
Non sequitur.  
March 26th, 2019, 09:54 AM  #4 
Newbie Joined: Oct 2018 From: Indoors Posts: 12 Thanks: 0  
March 26th, 2019, 11:19 AM  #5  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,276 Thanks: 944 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
What part of it do you not understand? We can't help you if we don't know! Dan  
March 26th, 2019, 11:33 AM  #6 
Senior Member Joined: Dec 2015 From: somewhere Posts: 647 Thanks: 94 
I thought that it was a standard graph and not polar graph. To ‘topsquark’ : can i change my name and how ? ‘idontknow’ sounds like nonsense. 
March 26th, 2019, 11:51 AM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,276 Thanks: 944 Math Focus: Wibbly wobbly timeywimey stuff.  

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