# Spherical-coordinates

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##### Intros
###### Lessons
1. Spherical Coordinates Overview:
2. Spherical Coordinates
• Instead of $(x,y,z)$, we have $(\rho,\theta,\varphi)$
• 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:

$(2,5,1)$

1. Convert the following Cartesian Point into Spherical Coordinates:

$(-2,-1,-4)$

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

$x^2 + y^2 - 2y = 3$

1. Convert the following Cartesian Equation into Spherical Coordinates:

$\frac{x}{z} = \frac{y}{x}$

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

$\rho^2 = \sin\varphi \cos\theta$

1. Convert the following Spherical Equation into Cartesian Coordinates

$\csc \varphi = \rho \sin \theta + \rho \cos \theta$

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

$\rho^2 = 2\rho \sin\varphi \sin\theta + 4$