1. ## Contour Map

I am fairly familiar with contour maps in the form f(x,y).

But there is this problem:
f(r,theta) = 1+sin(theta)-r with z = 1,3/4,1/2,1/4,0.

I was thinking about transforming that into rectangular coordinates and somehow solve it that way, but even so, I do not know how to convert that.

i TRIED to convert it and got y = root [(z-sin(theta)-1)^2-x^2]. If that is correct. how would I even map that?

2. Do you have any polar graph paper? That would make it easy to graph. Just set f(r,theta) equal to each of your z's and then solve for r in terms of theta. So for instance:

z = 1 = 1+ sin(T) - r ----> r = sin(T)

So start at theta=0 on your polar graph paper and then work your way counterclockwise calculating r along the way. Then do this for each z.

Alternatively, if you must have cartesian coordinates, remember:

r = (x^2+y^2)^(1/2)
sin(T) = y/r = y*(x^2+y^2)^(-1/2)

then f(r,theta) -> f(x,y) = 1 + y*(x^2+y^2)^(-1/2) - (x^2+y^2)^(1/2) = $\displaystyle 1-\frac{x^2+(y-1) y}{\sqrt{x^2+y^2}}$

Good luck solving this for z... better stick with polar coordinates. Most calculators can be set into polar coordinates too.

3. ## another question

thank you, i drew the contour map and i guess it's correct.

however, another question came up and it was, based on the contours in the previous problem, sketch the graph of the function f(r,theta) = 1+sin(theta)-r
(same function) but for 0< f(r,theta) <1

Isn't this the same thing as the previous problem? because from 0 to 1 is basically all the z values.