 # Provide notes on how triple integrals defined in cylindrical and spherical coordinates and the reason to prefer one of these coordinate systems to working in rectangular coordinates. tinfoQ 2021-02-05 Answered
Provide notes on how triple integrals defined in cylindrical and spherical coordinates and the reason to prefer one of these coordinate systems to working in rectangular coordinates.
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it Gennenzip
Cylindrical coordinates prefer represent a point P in space by ordered triples in which r and $\theta$ are polar coordinates for the vertical projection of P on the $xy=pla\ne ,$ with , and x is the rectangular vertical coordinate.
The equations relating rectangular and cylindrical coordinates are,
$x=r\mathrm{cos}\theta$
$y=r\mathrm{sin}\theta$
$z=z$

$\mathrm{tan}\theta =\frac{y}{x}$
The spherical coordinates represent a point P in by ordered triples $\left(\rho ,\varphi ,\theta \right)$ in which,
$\rho$ is the distance from P to the origin
. $\varphi$ is the angle $over\to \left\{OP\right\}$ makes with the positive z - axis
. $\theta$ is the angle from cylindrical coordinates.
The equations relating spherical coordinates to Cartesian and cylindrical coordinates are,
$r=\rho \mathrm{sin}\varphi$
$x=r\mathrm{cos}\theta =\rho \mathrm{sin}\varphi \mathrm{cos}\theta$
$z=\rho \mathrm{cos}\varphi$
$y=r\mathrm{sin}\theta =\rho \mathrm{sin}\varphi \mathrm{sin}\theta$

$\mathrm{tan}\theta =\frac{y}{x}$
Cylindrical coordinates are good for describing cylinders whose axes run along the z - axis and planes that either contain the z - axis or lie perpendicular to the z -axis.
Surfaces like these have equations of constant coordinate value.

We have step-by-step solutions for your answer!