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