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