Matlab polar to rectangular coordinates

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SUMMARY

The discussion focuses on creating a MATLAB function to convert polar coordinates to rectangular coordinates in two-dimensional space. The function takes two input vectors: one for the radius and another for the angle in radians, both containing at least five elements. The output consists of two vectors representing the x and y coordinates. The conversion formulas used are x = r * cos(θ) and y = r * sin(θ), and the script includes a formatted table displaying both the original polar coordinates and the converted rectangular coordinates.

PREREQUISITES
  • Understanding of MATLAB programming and syntax
  • Familiarity with polar and rectangular coordinate systems
  • Knowledge of trigonometric functions: cosine and sine
  • Ability to format output in MATLAB for table display
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  • Learn how to create and manipulate vectors in MATLAB
  • Explore MATLAB's built-in functions for trigonometric calculations
  • Research MATLAB table formatting and display options
  • Study the use of function m-files in MATLAB for modular programming
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Students, educators, and professionals working with MATLAB who need to convert polar coordinates to rectangular coordinates, as well as anyone interested in enhancing their programming skills in MATLAB.

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Prepare a function m-file containing a function that converts polar coordinates in two-dimensional space to rectangular (Cartesian) coordinates. Include a suitable H1 line and some additional comment lines. The input will be 2 vectors, and the output will be 2 vectors. The length of each vector (on input and on output) will equal the number of points whose conversion from polar to rectangular coordinates is required.

The radius of a point will appear as an element in the first input vector, and the angle (in radians) of that point will appear as the corresponding element in the second input vector. The first output vector will contain the horizontal (x) coordinates, and the second output vector will contain the vertical (y) coordinates.

In the first section of your script m-file, generate 2 input vectors that you will use to test your function. Use at least 5 points, with any values you want. (Each input vector should be of length 5 or greater.) Then call your function to do the coordinate conversions. Finally, print a table. Each row in the table will correspond to one point. The first 2 columns (of 4 columns in the table) should contain the original polar coordinates, and the last 2 columns should contain the equivalent rectangular coordinates. Use formatted printing. The decimal points in each column should all lie on one vertical line.

Sorry for the super long question but I am fully lost on how to approach this. I'd really appreciate help on it.
 
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I'm not quite as up on my MATLAB as all that, but the equations to convert from polar to rectangular are as follows. Given the magnitude $r$ and direction $\theta$ (which is the angle the vector makes with the positive $x$ axis), the components are given by
\begin{align*}
x&=r \cos(\theta), \\
y&=r \sin(\theta).
\end{align*}
The rest of this problem, it seems to me, is formatting.
 

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