My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Thanks Tree1Thanks
  • 1 Post By topsquark
Reply
 
LinkBack Thread Tools Display Modes
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.
TheReluctantMathMan is offline  
 
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.
idontknow is offline  
March 22nd, 2019, 09:00 AM   #3
Newbie
 
Joined: Oct 2018
From: Indoors

Posts: 12
Thanks: 0

Quote:
Originally Posted by idontknow View Post
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 View Post
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.
TheReluctantMathMan is offline  
March 26th, 2019, 09:54 AM   #4
Newbie
 
Joined: Oct 2018
From: Indoors

Posts: 12
Thanks: 0

http://m.wolframalpha.com/input/?i=p...%28theta%29%29
Anyone?
TheReluctantMathMan is offline  
March 26th, 2019, 11:19 AM   #5
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 2,276
Thanks: 944

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by idontknow View Post
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 View Post
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
Thanks from idontknow
topsquark is offline  
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.
idontknow is offline  
March 26th, 2019, 11:51 AM   #7
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 2,276
Thanks: 944

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by idontknow View Post
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
topsquark is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
gaphs, polar



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Polar math problem regarding tangents to a polar curve sanchay09 Calculus 5 October 10th, 2013 12:21 AM
Polar Coordinates Britwells Algebra 9 March 28th, 2013 12:58 PM
Polar curve Agata78 Algebra 7 January 20th, 2013 02:05 PM
polar differentiation waytogo Calculus 0 October 23rd, 2010 11:47 AM
Polar math problem regarding tangents to a polar curve sanchay09 Algebra 1 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.