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?