My Math Forum Polar gaphs

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 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 = 1-sin(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,pi-x) and we get r = 1+sin(pi-x) 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 = 1-sin(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
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Quote:
 Originally Posted by idontknow 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 .
What're you high?

Quote:
 Originally Posted by idontknow 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 $\displaystyle c=\pm 1$ .
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
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Quote:
 Originally Posted by idontknow 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 $\displaystyle c=\pm 1$ .
Quote:
 Originally Posted by TheReluctantMathMan What're you high?
I take it by your slightly rude comment that you don't understand idontknow's post?

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
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 Originally Posted by idontknow 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.
You'd have to talk to a Mod for that. (Greg's pretty amenable.) But I don't know if it's possible.

-Dan

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