Re: polar and cartesian

In article <1158034018.049981.21010@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
vicky <vikash.vks123@xxxxxxxxx> wrote:
Friends
As we knowrelation between poler and cartesian co-ordinates are
x=r*cos(t) -------(1) // sorry i
use t for angle theta//

Nothing to be sorry for...

y=r*sin(t) --------(2)
r ^2= x^2+y^2 -------(3)
t= tan^-1(y/x) -------(4)

No, you can take t = arctan(y/x) if x > 0, but if x < 0 you want
arctan(y/x) (+/-) pi (depending on which interval you want it to be in),
and if x = 0 the arctan is undefined.

By equation (1) x_r = cos(t) ----(5)

OK, if _r means partial derivative wrt r (keeping t constant).

By equation (3) differentiating w.r.to r we get
x_r= sec(t) -------(6)

"We" don't. The partial derivative of (3) wrt r (keeping t
constant) is

2 r = 2 x x_r + 2 y y_r
= 2 r cos(t) x_r + 2 r sin(t) y_r

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada



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Relevant Pages

  • polar and cartesian
    ... As we knowrelation between poler and cartesian co-ordinates are ... use t for angle theta// ... By equation differentiating w.r.to r we get ...
    (sci.math)
  • Re: polar and cartesian
    ... As we knowrelation between poler and cartesian co-ordinates are ... use t for angle theta// ... By equation differentiating w.r.to r we get ...
    (sci.math)