This is a problem that has been bugging me all day. While working with the well-known dydx = rdrdθ, where r is a function of θ I divided both sides of the equation by dxdθ to get dy/dθ = r(dr/dx)(adsbygoogle = window.adsbygoogle || []).push({});

For the left side, I use y = rsinθ and derive with respect to θ to get dy/dθ = sinθdr/dθ + rcosθ. For the left side, I use r^2 = y^2 + x^2, and derive both sides dx, to get

2r(dr/dx)=2y(dy/dx) + 2x, which simplifies to r (dr/dx)=y(dy/dx) + x.

I then put both of these equalities in the equation to get

sinθ(dr/dθ) + rcosθ = y(dy/dx) + x. Knowing that x = rcosθ, and that y/r = sinθ

I subtract x then divide y from both sides to get

(1/r)(dr/dθ) = (dy/dx).

However, this contradicts the proof that

dy/dx =((dr/dθ)sinθ+rcosθ)/((dr/dθ)cosθ-rsinθ).

I just want to know what went wrong. (I have checked mathematically, these two functions will NOT give the same results at most points.)

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Polar and cartesian issue

Tags:

**Physics Forums | Science Articles, Homework Help, Discussion**