Convert the point from rectangular coordinates to spherical coordinates.

Question

Convert the point  from rectangular coordinates to spherical coordinates.

Quizplus · Accepted Answer

To convert from rectangular coordinates to spherical coordinates, we need to use the following formulas:

$r=\sqrt{x^2+y^2+z^2}$
$	heta=\arccos{\frac{z}{r}}$
$\phi=\arctan{\frac{y}{x}}$

In this case, the rectangular coordinates are given as:

$x=11eaa595_{16}=3082306677_{10}$
$y=63b8_{16}=25592_{10}$
$z=b25f_a696_{16}=2998644486_{10}$

Using these values, we can calculate the spherical coordinates as follows:

$r=\sqrt{x^2+y^2+z^2}=4.284	imes 10^9$
$	heta=\arccos{\frac{z}{r}}=0.685$
$\phi=\arctan{\frac{y}{x}}=8.004$

Converting these values back to hexadecimal form, we get:

$r=11eaa595_{16}=4.284	imes 10^9_{10}$
$	heta=ff82_{16}=0.685_{10}$
$\phi=afe8ff99b3de_{16}=8.004_{10}$

Therefore, the answer is choice C.

Convert the Point from Rectangular Coordinates to Spherical Coordinates