How can I convert coordinates from Spherical to Cartesian?

[Mathysics]

I do not understand Spherical coordinate system.

I'm asked to compare the differences with Cartesian coordinate but I have no idea how to start.

So I would like some help that will at least give me a understanding of the spherical coordinate system, thx

 

[Cyosis]

Let's stick to the 2-d case first. That means we compare Cartesian coordinates with polar coordinates. In Cartesian you need an x coordinate and a y coordinate to describe a fixed point on the grid. How do you describe such a point in polar coordinates?

 

[Mathysics]

Let's stick to the 2-d case first. That means we compare Cartesian coordinates with polar coordinates. In Cartesian you need an x coordinate and a y coordinate to describe a fixed point on the grid. How do you describe such a point in polar coordinates?

(magnitude,angle)

The task is to investigate the spherical coordinate system, which I haven't learn but I have no idea what to do

 

[Cyosis]

Yes it's the distance to that point and an angle. Keeping the distance to a point constant while rotating the angle 2pi rad you will get a circle. How can you extend this system so that instead of a circle you get a sphere?

 

[Hootenanny]

Wikipedia and Wolfram's Mathworld have pretty good pages on spherical coordinates, I would suggest that you try having a look there.

 

[HallsofIvy]

I'm now starting to understand more about spherical coordinate system. I had been researching information about spherical coordinate system but now I am stuck again :)

To convert φ from Spherical to Cartesian we can use φ = arctan (y/x)

The problem is... I don't know how to do arctan so I like some help again.

If my points are (3,4,5) how can i convert that into φ using the formula above?

You put those numbers into the formula and do exactly what the formula says! y= 4 and x= 3 so y/x= 4/3. What is arctan(4/3)?