## Quick Reference

Suppose that three mutually perpendicular directed lines *Ox*, *Oy* and *Oz*, intersecting at the point *O* and forming a right-handed system, are taken as coordinate axes. For any point *P*, let *M* and *N* be the projections of *P* onto the *xy*-plane and the *z*-axis respectively. Then *ON*=*PM*=*z*, the *z*-coordinate of *P*. Let ρ=| PN |, the distance of *P* from the *z*-axis, and let *ϕ* be the angle ∠ *xOM* in radians (0≤*ϕ*<2 *π*). Then (*ρ*, *ϕ*, *z*) are the cylindrical polar coordinates of *P*. (It should be noted that the points of the *z*- axis give no value for *ϕ*.) The two coordinates (*ρ, ϕ*) can be seen as polar coordinates of the point *M* and, as with polar coordinates, *ϕ*+2*kπ*, where *k* is an integer, may be allowed in place of *ϕ*.The Cartesian coordinates (*x*, *y*, *z*) of *P* can be found from (*ρ, ϕ*, *z*) by: *x*=*ρ* cos *ϕ*, *y*=*ρ* sin *ϕ*, and *z*=*z*. Conversely, the cylindrical polar coordinates can be found from (*x*, *y*, *z*) by: is such that and and *z*=*z*. Cylindrical polar coordinates can be useful in treating problems involving right-circular cylinders. Such a cylinder with its axis along the *z*-axis then has equation *ρ*=constant.

*Subjects:*
Mathematics.

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