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Spherical Coordinate System. The spherical coordinate system specifies the position of a point P by the combination of its distance to the origin (radius r), the angle φ between the x-axis and the line OQ, and the angle θ between the radius and the z-axis.

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We'll cover three ways of describing the location of a point: with rectangular coordinates, cylindrical coordinates, and spherical coordinates. There are other coordinate systems (including some wacky ones like hyperbolic and spheroidal coordinates), but these are the ones that are most commonly used for three dimensions.

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Polar Coordinates side 1 In class, we use Cartesian coordinates for all our work. Most of the time, this is the easiest coordinate system to use. It is important to realize that the choice of a coordinate system should make the problem easier to use. We see this when we do problems involving inclined

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A plane wave satisfies the one-dimensional wave equation in Cartesian coordinates. {\partial^2\psi\over\partial t^2} = v^2 {\partial^2\psi\over\partial z^2}. To obtain plane waves, the position vector must remain perpendicular to a give plane. Pick a point on the plane \mathbf{r}_{0}.

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Calculation of a triple integral in Cartesian coordinates can be reduced to the consequent calculation of three integrals of one variable. Consider the case when a three dimensional region \(U\) is a type I region, i.e. any straight line parallel to the \(z\)-axis intersects the boundary of the region \(U\) in no more than \(2\) points.