Convert Cartesian coordinates to spherical shape

[baby_1]

Hello
how can Convert Cartesian coordinates to spherical with shape?
for clear my question i explain a way to convert my coordinates in different spherical.
for example i use this diagram to convert Cartesian coordinates to Cylindrical(with image to axises)

for example:

now how can i do the same approach for spherical? does we have a simple shape for image the axises?

Thanks

 

[Fredrik]

You have made it pretty hard to understand what you mean. I would guess that you're talking about polar coordinates (for $\mathbb R^2$), not cylindrical (for $\mathbb R^3$), and that what you meant by $\hat{ay}$ is a unit vector in the direction of increasing y coordinate. You probably wanted to write $\hat{a}_y$.

I would recommend that you start by checking out Wikipedia's article on these coordinate systems:

http://en.wikipedia.org/wiki/Polar_coordinate_system
http://en.wikipedia.org/wiki/Cylindrical_coordinate_system
http://en.wikipedia.org/wiki/Spherical_coordinate_system