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## Homework Statement

Consider z=f(x,y), where x=rcosθ and y=rsinθ

(This is a multi part multi variable calculus assignment question). I've just derived dz/dr and now I'm asked... to show that [itex]r^{2}=x^{2}+y^{2},

\theta=a\tan(\frac{y}{x})[/itex]

## Homework Equations

## The Attempt at a Solution

I've drawn up a triangle with r as the hypotenuse, x on the x axis, y on the y axis.

and then x=rcosθ=r * x/r = x by trig laws and then [itex]r^{2}=x^{2}+y^{2}[/itex] by pythagoras theorem etc

this seems too easy. is there some other way to show this?