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Math Help - Find cartesian and cylindrical coordinates from sypherical

  1. #1
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    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?
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  2. #2
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    \sin \frac{\pi}{4}=\cos \frac{\pi}{4}=\frac{\sqrt{2}}{2}

    You shouldn't approximate these values unless specifically asked to.
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  3. #3
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    Where am I going wrong though when sin(pi/4)=1/sqrt(2) and cos(pi/2)=0

    I am confused
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  4. #4
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    I'm not sure what you mean. What do you think is wrong?
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  5. #5
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    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
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  6. #6
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    x is 0.

    \tan \frac{\pi}{2} is undefined.
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  7. #7
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    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.
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  8. #8
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    By the way, \theta is the same in spherical and cylindrical. You've been over-thinking how to find it.
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