Question

Cartesian and polar coordinates are related through the transformation equations
{x = r cos Theta or {r^2= x^2 + y^2
{Y = r sin theta { tan theta = y/x

A. Evaluate the partial derivatives Xr, Yr,Xtheta, and Ytheta.
B. Evaluate the partial derivatives Rx, Ry, Theta x, Theta y.
C. For a function z = f(x,y), find z, and Ztheta, where x and y are expressed in terms of r and theta.
D. for a function z = g(r,theta), find Zx, and Zy, where r and theta are expressed in terms of x and y.
E. show that (∂z/∂x)^2 + (∂z/∂y)^2 = (∂z/∂r)^2 + 1/r^2 (∂z/∂theta)^2

Answer 1

polars give me a headache still :)

Answer 2

we haven't learned this and she gives it as a quiz problem smh

Answer 3

a and b are simple enough id think

Answer 4

z is a circle

Answer 5

lol i am not that smart. still trying to figure out the answer for other one

Answer 6

partials mean that the only thing changing is variable we are diffing with. wrt to r means that every thing that aint r is not changing, when things dont change they are consant.

Xr = cos(t) ; Yr = sin(t)

Answer 7

x = r cos(t) ; Xr means that only r changes, everything else remains consant

Xr = cos(t) then

Answer 8

Xt would mean that r doesnt change and remains constant ....

Xt = -r sin(t)

Answer 9

this is for a and b right

Answer 10

that is the concepts behind a and b yes

Answer 11

yea

Answer 12

z = f(x,y); this ones a bit vague to me since it really doesnt provide us with a structure for f(x,y) other than to assume we use x and y in the rule for the function

Answer 13

z = xy - x^2 +3y would be a function of z in x and y

Answer 14

if we allow z to mimic the results of the vector function: z =<rcos(t),rsin(t)> we get a circle centered at the origin of radius r

Answer 15

i am so confused

Answer 16

to which: z^2 = r^2 -(x/r)^2 -(y/r)^2

Answer 17

lol, im just a little confused ;)

Answer 18

lol i have no clue whats going on

Answer 19

yeah, after a and b im lost :) srry

Answer 20

i am even lost on a and b