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Spherical-coordinates

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Intros
Lessons
  1. Spherical Coordinates Overview:
  2. Spherical Coordinates
    • Instead of (x,y,z)(x,y,z), we have (ρ,θ,φ)(\rho,\theta,\varphi)
    • Graph of the coordinates in 3D
  3. Equations to Convert from Cartesian to Spherical
    • Finding the Equations
    • Trig Ratios, Pythagoras
    • Using Equations from last section to obtain more equations!
  4. Example of Converting Equations
    • Cartesian to Spherical
    • Spherical to Cartesian
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Examples
Lessons
  1. Converting Cartesian Points into Spherical Coordinates
    Convert the following Cartesian Point into Spherical Coordinates:

    (2,5,1)(2,5,1)

    1. Convert the following Cartesian Point into Spherical Coordinates:

      (−2,−1,−4)(-2,-1,-4)

      1. Converting Cartesian Equations into Spherical Coordinates
        Convert the following Cartesian Equation into Spherical Coordinates:

        x2+y2−2y=3x^2 + y^2 - 2y = 3

        1. Convert the following Cartesian Equation into Spherical Coordinates:

          xz=yx\frac{x}{z} = \frac{y}{x}

          1. Converting Spherical Equations into Cartesian Coordinates
            Convert the following Spherical Equation into Cartesian Coordinates:

            ρ2=sin⁡φcos⁡θ\rho^2 = \sin\varphi \cos\theta

            1. Convert the following Spherical Equation into Cartesian Coordinates

              csc⁡φ=ρsin⁡θ+ρcos⁡θ\csc \varphi = \rho \sin \theta + \rho \cos \theta

              1. Graphing the Spherical Equations by Changing into Cartesian Coordinates
                Graph the following Spherical Equation in the Cartesian Plane.

                ρ2=2ρsin⁡φsin⁡θ+4\rho^2 = 2\rho \sin\varphi \sin\theta + 4