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 Trigonometry Trigonometry Math Forum

 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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Quote:
 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 Tags gaphs, polar Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post sanchay09 Calculus 5 October 10th, 2013 12:21 AM Britwells Algebra 9 March 28th, 2013 12:58 PM Agata78 Algebra 7 January 20th, 2013 02:05 PM waytogo Calculus 0 October 23rd, 2010 11:47 AM sanchay09 Algebra 1 December 31st, 1969 04:00 PM

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