Show that r^2 = x^2 + y^2

  • #1

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?
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,670
Not unless you want to prove the Pythagorean Theorem itself.
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770

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]

That doesn't have anything to do with ##z = f(x,y)##. It's just standard polar coordinate equations.$$
x^2 + y^2 = r^2\cos^2\theta + r^2\sin^2\theta = r^2$$ $$
\frac y x = \frac{r\sin\theta}{r\cos\theta}=\tan\theta$$
 
  • #4
yeah that's why I was confused. I don't get how I'm showing that by just plugging it into equations and referring to the polar equations.
 

Related Threads on Show that r^2 = x^2 + y^2

Replies
5
Views
4K
Replies
2
Views
2K
Replies
7
Views
7K
Replies
12
Views
828
Replies
6
Views
12K
Replies
16
Views
3K
Replies
15
Views
3K
  • Last Post
Replies
2
Views
834
Top