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) x2 + y2 = x (b) y2 = 2x 2. Relevant equations r2 = x2 + y2 Tan(T) = y/x, where (T) stands in for theta 3. The attempt at a solution For the first one, I found r = x1/2, aka sqrt (x), but am completely stumped on what to do about finding theta. Arctan (sqrt(x - x2) / (x2 + y2))... 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 cos2(T) + x sin2(T) = sqrt(x) cos(T). Factoring out an x, the cos2 + sin2 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) / sin2(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(x2 + 2x). Again, no idea how this is supposed to be useful.