# Thread: Find cartesian and cylindrical coordinates from sypherical

1. ## 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?

2. $\sin \frac{\pi}{4}=\cos \frac{\pi}{4}=\frac{\sqrt{2}}{2}$

You shouldn't approximate these values unless specifically asked to.

3. Where am I going wrong though when sin(pi/4)=1/sqrt(2) and cos(pi/2)=0

I am confused

4. I'm not sure what you mean. What do you think is wrong?

5. 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

6. x is 0.

$\tan \frac{\pi}{2}$ is undefined.

7. 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.

8. By the way, $\theta$ is the same in spherical and cylindrical. You've been over-thinking how to find it.