OK, so I have the following polar equation:
$r = Θ/20$
And I would like to translate this a little to the right, and down from the polar origin.
Now, I figure since I know cartesian coordinate equation translations are quite simple, the best way to do this would be to convert this polar equation to a rectangular equation, translate, and then convert back to polar again.
However, I was having some problems making the initial conversion.
I know we are supposed to use the following relationships between polar and rectangular equations:
$r^2 = x^2 + y^2$
$y = rsin(Θ)$
But, I cannot seem to convert my equation correctly…
Would someone be able to suggest a simpler way to make this translation?
Or, assist me in converting to polar and back again?
I'm quite new at this, so I apologize if this question is remedial.
Thanks!
Best Answer
The other equation you need is $\theta = \arctan \frac {y}{x}$ and you have to worry about the branches of arctan. So now you have $\sqrt{x^2+y^2}=\frac{1}{20} \arctan \frac {y}{x}$. To translate right and down, you replace $x$ with $x+a$ and $y$ with $y-b$. And you have quite a mess. Taking $\sqrt{(x+a)^2+(y-b)^2}=\frac{1}{20} \arctan \frac {y-b}{x+a}$ back to polar is a lot of work and probably not illuminating.