with(plots):

a:=polarplot(3-3*cos(theta),theta=0..2*Pi):

c:=plot((3*sqrt(2)+3)/2 + ((-3*sqrt(2))/(-3*sqrt(2)-6))*(x+((3*sqrt(2)+3)/2)),x=-10..10):

display(a,c,view=[-10..10,-10..10]);

a:= is the polar plot of the cardiod (3-3cos(theta)

In order to plot the tangent line to the cardiod in theta= 3Pi/4, I find the point (x,y) in rectangular coord x=(3-3cos(theta)cos(theta) and y=(3-3cos(theta)sin(theta); then I find the derivative of dx/dy=

[(3-3*cos(theta)*cos(theta)+sin(theta)(3sin(theta)]/[-(3-3cos(theta)sin(theta)+cos(theta)(3sin(theta)]and from here I get the slope.So I can plot c:= tangent line to the cardiod in 3Pi/4.

How can I avoid having to convert everyting to rectangular coords, and plot the tangent line in polars?

Maple 10 does not have intersectplots.

The first surface is x^2+y^2+z^2=9 and the second one is x^2+y^2+(z-3)^2=9

I have an electric field as a function of time and space.It is a uniform plane wave.

E(r,t)= 3*cos(w*t-k*z+Pi/4)x+ 2*sin(w*t-k*z-Pi/3)y

where r is the space vector r=xx+yy+zz; 

x   y and z are unit vectors.

w and k are constants.

How can I plot it?

How can I plot the intersection of x^2+y^2+z^2<=9 and x^2+y^2+(z-3)^2<=9?

Is the intersection of this two equations a 3D region?

Thanks.