![]() ![]() We can calculate the relationship between the Cartesian coordinates $(x,y,z)$ of the point $P$ and its spherical coordinates $(\rho,\theta,\phi)$ using trigonometry. Lastly, $\phi$ is the angle between the positive $z$-axis and The angle between the positive $x$-axis and the line segment from the origin Point $Q$ is the projection of $P$ to the $xy$-plane, then $\theta$ is The coordinate $\rho$ is the distance from $P$ to the origin. Spherical coordinates are defined as indicated in theįollowing figure, which illustrates the spherical coordinates of the Relationship between spherical and Cartesian coordinates On this page, we derive the relationship between spherical and Cartesian coordinates, show an applet that allows you to explore the influence of each spherical coordinate, and illustrate simple spherical coordinate surfaces. The following graphics and interactive applets may help you understand sphericalĬoordinates better. But some people have trouble grasping what the If one is familiar with polar coordinates, then the angle $\theta$ isn't too difficult to understand as it is essentially the same as the angle $\theta$ from polar coordinates. ![]() Spherical coordinates determine the position of a point in three-dimensional space based on the distance $\rho$ from the origin and two angles $\theta$ and $\phi$. Spherical coordinates can be a little challenging to understand at first.
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