# Find cartesian and cylindrical coordinates from sypherical

• Feb 8th 2011, 04:41 PM
operaphantom2003
Find cartesian and cylindrical coordinates from sypherical
Can someone please tell me where I am going wrong on this? I think it has to do with my x value.

Let P be the point with the spherical coordinates ρ=8,φ=π/4,θ=π/2. A. The cylindrical coordinates of P are r= , θ= , z= . B. The cartesian coordinates of P are x= , y= , z= .

Here is what I have so far:
spherical to cartesian:
x=ρ sin(φ)cos(θ)
y=ρ sin(φ)sin(θ)
z=ρ cos(φ)

so I have
x=(8)(.7071067812)(0)=0
y=(8)(.7071067812)(1)=5.656854249
z=(8)(.7071067812)=5.656854249

cartesian to cylindrical
r=sqrt(x^2+y^2)
θ=tan^(-1) * y/x
z=z

so I have
r=sqrt((0^2)+(5.656854249)^2))= 31.99999999
θ= ****can't divide by 0****
z=5.656854249

Where am I going wrong?
• Feb 8th 2011, 05:44 PM
DrSteve
$\sin \frac{\pi}{4}=\cos \frac{\pi}{4}=\frac{\sqrt{2}}{2}$

You shouldn't approximate these values unless specifically asked to.
• Feb 8th 2011, 06:13 PM
operaphantom2003
Where am I going wrong though when sin(pi/4)=1/sqrt(2) and cos(pi/2)=0

I am confused :(
• Feb 8th 2011, 06:20 PM
DrSteve
I'm not sure what you mean. What do you think is wrong?
• Feb 8th 2011, 06:23 PM
operaphantom2003
If cos(pi/2)=0 then x=0 but to find theta I would be dividing by 0 and you can't do that. I must be making a mistake finding x but isn't it x=8*1/sqrt(2)*0....so x=0
• Feb 8th 2011, 07:32 PM
DrSteve
x is 0.

$\tan \frac{\pi}{2}$ is undefined.
• Feb 8th 2011, 07:36 PM
operaphantom2003
It says that answer is incorrect. I am about ready to give up on this problem. Glad to know I was working the problem correctly though. Thanks for all the help.
• Feb 8th 2011, 07:39 PM
DrSteve
By the way, $\theta$ is the same in spherical and cylindrical. You've been over-thinking how to find it.