HW $6$

In $3$D space, the Cartesian coordinates $(x,y,z)$ can be converted to spherical coordinates $($radius $r,$ polar angle, $,$ azimuth angle, $)$ by the following equations:

$r=\sqrt[\phantom{2}]{x^2+y^2+z^2},=co{s}^{-1}(\frac{z}{r}),=ta{n}^{-1}(\frac{y}{x})$

Write a function fn$\_$printspherical that prints the Cartesian coordinates $(x,y,z)$ and corresponding spherical coordinates, $(r,,).$ The function $fn\_$ printspherical calls a subfunction fn$\_$convert$2$spher that converts from Cartesian to spherical coordinates.

Write a script, CartSpher that reads the Cartesian coordinates from an external file, convert to spherical coordinate, and print the results. When the script reads the Cartesian coordinates from a file, assume that $x,y,z$ are saved in matrix, thus fn$\_$printspherical should be in the loop to print all the results.

Here is the requirement for the script:

$xYZ.txt$

$\backslash$table$[[8\mathrm{.}1,1\mathrm{.}6,6\mathrm{.}6],[9\mathrm{.}1,9\mathrm{.}7,0\mathrm{.}4],[1\mathrm{.}3,9\mathrm{.}6,8\mathrm{.}5],[9\mathrm{.}1,4\mathrm{.}9,9\mathrm{.}3],[6\mathrm{.}3,8,6\mathrm{.}8],[1,1\mathrm{.}4,7\mathrm{.}6],[2\mathrm{.}8,4\mathrm{.}2,7\mathrm{.}4],[5\mathrm{.}5,9\mathrm{.}2,3\mathrm{.}9],[9\mathrm{.}6,7\mathrm{.}9,6\mathrm{.}6],[9\mathrm{.}6,9\mathrm{.}6,1\mathrm{.}7]]$

Read the file $($XYZ$.$txt$)$ by using the following function

$-$input $($Let user input file name$)$

$-$load $($read the file that user input$)$

When you load the data, assign the data values to the matrix variable. Use this matrix variable as input variable$($s$)$ to the function, fn$\_$printspherical

Display should follow the below format