Find (∂a/∂θ) given 3 equations

[MeMoses]

Homework Statement

Find (∂a/∂x) if
x = r*sin(a)*cos(θ),
y = r*sin(a)*sin(θ),
z =r*cos(a).
The equations originally have phi in place of a, but I switched it to a for ease of typing.

Homework Equations

Chain rule?

The Attempt at a Solution

I'm not exactly sure where to start. I tried using the chain rule and differentiating with respect to x but then I just end up with too many unknown and nothing really simplifies. How exactly does one go about solving this problem? Thanks ahead of time for any help.

 

[Mark44]

Homework Statement

Find (∂a/∂θ) if
x = r*sin(a)*cos(θ),
y = r*sin(a)*sin(θ),
z =r*cos(a).
The equations originally have phi in place of a, but I switched it to a for ease of typing.

Homework Equations

Chain rule?

The Attempt at a Solution

I'm not exactly sure where to start. I tried using the chain rule and differentiating with respect to x but then I just end up with too many unknown and nothing really simplifies. How exactly does one go about solving this problem? Thanks ahead of time for any help.

Unless I'm missing something here, ∂\phi/∂θ = 0, which is the case whenever you have partials involving two independent variables.
The equations you gave above are just the equations to convert from spherical coordinates to rectangular (or Cartesian) coordinates (but r should be replaced by ρ). In spherical coordinates, \phi and θ have no connection, so neither is a function of the other, making them independent variables.

 

[MeMoses]

crap I meant Find (∂ϕ/∂x) which should make more sense and explains why I tried differentiating with respect to x. Now that that's clear where exactly do I start?