Is it as simple as just plugging in phi=pi/6 into the relavant forumula relating spherical and cylindrical, and spherical and cartesian coordinates? And leaving as it is, with say rho and theta still in the equation?
Hey everyone, I really need some help on this one, I just can seem to find a connection anywhere between formulas for each coordinate system.
Convert from spherical coordinates in to both Cartesian coordinates and cylindrical coordinates.
Can anyone help me at all?
Thanks again.
spherical coordinates refers to an angle inscribed on a circle of unit length. So the polar coordinates og your point will be (1,pi/6). Now we know that x^2+y^2=1 and tan^-1(x/y)=pi/6. solving both of them we get your point in cartesian system as (+-sqrt(3)/2,+-1/2). hope your are comfortable with my notations. i have no latex installed and having some problem with uploading bmp files as well.
The aren't asking for a specific point, but for the equation satisfied by all points that for which [tex]\phi= \frac{\pi}{6}.
The connection between Cartesian (x, y, z) coordinates and Spherical ( , , ) coordinates is
.
With then and so that
Then and
.
So . That's the equation of the cone of all points satifying .
In cylindrical coordinates, so that equation is in cylindrical coordinates.