(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to help a friend with these two questions, but given that I haven't studied this material in over a decade, it's one of the topics I cannot recall at all.

Convert the following from rectangular to polar coordinates:

(a) x^{2}+ y^{2}= x

(b) y^{2}= 2x

2. Relevant equations

r^{2}= x^{2}+ y^{2}

Tan(T) = y/x, where (T) stands in for theta

3. The attempt at a solution

For the first one, I found r = x^{1/2}, aka sqrt (x), but am completely stumped on what to do about finding theta. Arctan (sqrt(x - x^{2}) / (x^{2}+ y^{2}))... yeah, I'm pretty sure that whole tangent thing is useless. Using the reverse procedure (polar to rectangular) gives [sqrt(x) cos (T)]^{2}+ [sqrt(x) sin(T)]^{2}= sqrt(x) cos(T). Then x cos^{2}(T) + x sin^{2}(T) = sqrt(x) cos(T). Factoring out an x, the cos^{2}+ sin^{2}identity just gives x = sqrt(x) cos(T), which is... I'm pretty sure it's what was already known.

For the second: No idea how the two relevant equations could even potentially be useful, but I did notice if you take the reverse procedure (going from polar to rectangular), then using x = r cos(T), y = r sin(T), then [r sin(T)]^{2}= 2 r cos(T). This eventually reduces to r = 2 cos(T) / sin^{2}(T), or r = 2 cot(T)csc(T), or any number of other expressions that leaves me none the wiser about what the polar coordinates are supposed to resemble.

I suppose if you substitute y = sqrt(2x), that gives r = sqrt(x^{2}+ 2x). Again, no idea how this is supposed to be useful.

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# Homework Help: Rectangular and Polar Coordinates with variables

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