January 31st, 2015, 05:20 AM  #1 
Senior Member Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4  Plotting
How do I begin to sketch the polar curve of $\displaystyle r=2θ $

January 31st, 2015, 05:30 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,600 Thanks: 2588 Math Focus: Mainly analysis and algebra 
Mark some points and join them up with curves. You will notice that the radius of the spiral increases by a fixed amount each revolution. 
January 31st, 2015, 07:56 AM  #3 
Senior Member Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 
Yep it came good. Now if I had to sketch the polar curve of $\displaystyle θ=\frac{π}{3} $ Assuming θ is positive, I know that would be equal to the graph of $\displaystyle y=(√ 3)(x) $ But since θ is equal to a negative number how does that affect my graph? 
January 31st, 2015, 08:28 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,818 Thanks: 1461 
$\displaystyle \theta = \frac{\pi}{3}$ $\displaystyle \tan{\theta} = \tan\left(\frac{\pi}{3}\right)$ $\displaystyle \tan{\theta} = \sqrt{3}$ $\displaystyle \frac{y}{x} = \sqrt{3}$ $\displaystyle y = \sqrt{3} \cdot x$ 
January 31st, 2015, 08:38 AM  #5 
Senior Member Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 
So its sort of inverted, Thanks 

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