My Math Forum Parametric to Polar conversion of Rose Curve

 Algebra Pre-Algebra and Basic Algebra Math Forum

 June 22nd, 2018, 11:29 PM #1 Newbie   Joined: Jun 2018 From: India Posts: 1 Thanks: 0 Parametric to Polar conversion of Rose Curve Hi, The main question revolves around the Rhodonea curve AKA rose curve. The polar equation given for the curve is r = cos(kθ). The parametric equation is x = cos(kθ)cos(θ), y = cos(kθ)sin(θ). Can anyone show me the conversion from the general parametric form to the general polar form? Basically, what I am looking for is the working. How did the parametric form get converted to polar? P.S. In the case that the aforementioned doesn't happen, even if you are able to find the general rectangular coordinate form for the given polar equation above, it will work for me. Thanks! Last edited by skipjack; June 24th, 2018 at 05:29 PM.
 June 23rd, 2018, 12:28 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 Math Focus: Calculus/ODEs I would use the parameter $\displaystyle t$ and: $\displaystyle x(t)=r\cos(t)$ $\displaystyle y(t)=r\sin(t)$ We are given: $\displaystyle r=\cos(k\theta)$ Hence: $\displaystyle x(t)=\cos(k\theta)\cos(t)$ $\displaystyle y(t)=\cos(k\theta)\sin(t)$
 June 23rd, 2018, 10:40 PM #3 Member   Joined: Oct 2017 From: Japan Posts: 60 Thanks: 2 The following video may be of interest.
June 24th, 2018, 05:34 PM   #4
Global Moderator

Joined: Dec 2006

Posts: 19,191
Thanks: 1649

Quote:
 Originally Posted by MarkFL I would use the parameter $\displaystyle t$ and . . .
Eh?

 June 24th, 2018, 06:06 PM #5 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 Math Focus: Calculus/ODEs Oops...I meant: $\displaystyle x(t)=\cos(kt)\cos(t)$ $\displaystyle y(t)=\cos(kt)\sin(t)$
 June 24th, 2018, 06:45 PM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 Math Focus: Calculus/ODEs Like this:

 Tags conversion, curve, parametric, polar, rose

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Fabion Real Analysis 2 October 25th, 2013 07:36 AM sanchay09 Calculus 5 October 10th, 2013 12:21 AM swm06 Algebra 2 April 13th, 2012 09:34 AM Takk Complex Analysis 1 January 13th, 2012 06:43 AM sanchay09 Algebra 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top