 # Convert between the coordinate systems. Use the conversion formulas and show work. Spherical: (8,frac{pi}{3}, frac{pi}{6}) Change to cylindrical. texelaare 2021-01-22 Answered
Convert between the coordinate systems. Use the conversion formulas and show work. Spherical: $\left(8,\frac{\pi }{3},\frac{\pi }{6}\right)$ Change to cylindrical.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it Elberte

Solution: The spherical coordinates are given by $\left(s,\varphi ,\psi \right)$

So here $s=8,\varphi =\frac{\pi }{3},\psi =\frac{\pi }{6}$

These co-ordinates can be converted into culindrical coordinates by. $r=s\mathrm{sin}\psi$
$\varphi =\varphi$
$z=s\mathrm{cos}\psi$

So,

$r=8\mathrm{sin}\left(\frac{\pi }{6}\right),\varphi =\frac{\pi }{3},z=8\mathrm{cos}\left(\frac{\pi }{6}\right)$

Thus,

$r=8\cdot \frac{1}{2},\varphi =\frac{\pi }{3},z=8\frac{\sqrt{3}}{2}$

Thus,

$r=4,$

$\varphi =\frac{\pi }{3},$

$z=4\sqrt{3}$