Help with Rectangualer and Polar Equations

Question

darkbluechocobo · Answer

Convert the following expression into an equivalent rectangular expression:$$3r=\frac{ 1 }{ \cos \theta }$$

darkbluechocobo · Answer

I am confused where to start because I haven't had an example of this question yet till now

anonymous · Answer

I thought @phi gave you the whole things, right? just copy his method

darkbluechocobo · Answer

Yes, but this one is arranged weirdly to me s:

anonymous · Answer

why? do something,

anonymous · Answer

ok, let's try, watch me !! hehehe.. I 've just learned from phi
$r = \dfrac{1}{3cos \theta}$

darkbluechocobo · Answer

Hmm so we could put it back into its original form by doing 3rcosTheta

anonymous · Answer

$x =r cos \theta = \dfrac{1}{3}$, hence $x^2 =\dfrac{1}{9}$
$y = r sin \theta =\dfrac{1}{3} tan\theta$, thence $y^2= \dfrac{1}{9} tan^2\theta$

anonymous · Answer

$x^2+y^2 = \dfrac{1}{9} sec^2\theta$

anonymous · Answer

@OOOPS you went too far. The only variables in a rectangular form equation are x and y. The equation is simply x = 1/3

anonymous · Answer

see ??? something pops up, hehehe

darkbluechocobo · Answer

So basically just rearrange the equation so that it is rcostheta and rsintheta?

anonymous · Answer

@peachpi  really? oh, I am sorry. I talked too much. I am waiting for you to solve it. hehehe

darkbluechocobo · Answer

So would we take the squares

anonymous · Answer

@OOOPS you already solved it. You just don't have to square the x or involve y

anonymous · Answer

For this problem you don't need to square anything because you can eliminate the Θ without squaring

anonymous · Answer

I don't get it. r is a function with respect to theta. When converting to x, y, we should have function y with respect to x. 
if we stop at x = 1/3, then the function is a constant one while the corresponds one is not
r = 1/(3cos theta) is not a constant function.

anonymous · Answer

Very rarely will polar equations give y as a function of x. They usually relate y and x, but often don't pass the vertical line test. This particular polar equation is for the vertical line x = 1/3. That's why there's no y in the equation. x is constant. y, r, and Θ are not.

anonymous · Answer

Thanks for making it clear

anonymous · Answer

np. check out his write up for more info http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx