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## Homework Statement

Convert the vector given in spherical coordinates to cylindrical coordinates:

[tex] \vec{F}(r,\theta,\varphi) = \frac{F_{0}}{arsin\theta}\bigg{[}(a^2 + arsin\theta cos\varphi)(sin\theta \hat{r} + cos\theta \hat{\theta}) - (a^2 + arsin\theta sin\varphi - r^2 sin^2\theta) \hat{\varphi} \bigg] [/tex]

## Homework Equations

[tex] \theta [/tex] is elevation:

[tex] \rho = rcos\theta [/tex]

[tex] \varphi = \varphi [/tex]

[tex] z = rsin\theta [/tex]

## The Attempt at a Solution

I attempted to solve the problem by simple inserting all of the conversions into the spherical vector field. The problem was I keep on getting a bunch of r left that I don't know what to do. This is what I got by simply inserting the conversion above, I got them from https://en.wikipedia.org/wiki/Cylindrical_coordinate_system.

[tex] \vec{F}(\rho,\varphi,z) = \frac{F_{0}}{az}\bigg{[}(a^2 \frac{z}{r} + az\frac{z}{r}cos\varphi)\hat{\varphi} + (a^2 \frac{\rho}{r} + az\frac{\rho^2}{r^2})\hat{\varphi} - (a^2 + azsin\varphi - z^2)\hat{z}\bigg{]} [/tex]

Which I think is wrong since I have a lot of r's left. Can anyone make the conversion? I have tried for days.

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