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Convert from polar coordinates to rectangular coordinates using Matlab

Problem

A vector can be represented by its rectangular coordinates x and y or by its polar coordinates r and y. The relationship between them is given by the equations:
x = r*cos(θ)
y = r*sin(θ)

Solution

This problem has been taken from the book Practical Introduction to Matlab by Stormy Attaway. This is a very good book to read for people who are new to Matlab and also if you want to refresh yourself the concepts of Matlab, then this is a great book. This book assumes that you are new to Matlab and will teach you from beginning and make you a professional in Matlab programming. I suggest you read this book once if you really want to become a pro in Matlab.

You can learn about coordinate systems from here: Wikipedia - Coordinate system. If you know about the polarcoordinate system and Cartesian coordinate system and have learnt about it a long back then find the image below to brush yourself about the coordinate systems.
Image Credits: mathinsight.org
This problem is very simple. Before we solve this problem on Matlab type the following command:

 
help elfun


You can find that there are many elementary functions present in Matlab and some of them are sin, cos, tan, sind, cosd, tand and so on. I have mentioned only a few of them because they are important for us now, while remaining are also important but not necessary for solving this problem. I recommend you to have a glance at all the functions so that they will be useful for you in the future. Okay lets know what is the difference between sin and sind and in the similar way cos and cosd, tan and tand and so on. To be simple the difference is that sin assumes that the input parameter is in radians and on the other side sind assumes that the input is in degrees (‘d’ in sind represents degrees). So here let us assume that the user is giving input in radians as most of the mathematical problems corresponding to polar coordinates are in radians. You can also refer to the official documentation in the links below.
Coming back to problem, it is very simple because we are directly converting the equations given in the question to Matlab code. Have a look at the program first and if you still don’t understand then refer to the explanation section below the program section and I am sure you will understand the solution perfectly. Some of the concepts used in the program to solve the above problem are as follows:
1) Request User Input - Input Function
2) cos
3) sin
4) fprintf function
5) Elementary functions in Matlab

Program

%This program is for converting the polar co ordinates
%To cartesian co ordinates
 
%User input for the angle
angle = input('Enter the Angle of the polar coordinates: ');
 
%User input for r
r = input('Enter the value of "r": ');
 
%Convert according to equations given
x = r*cos(angle);
y = r*sin(angle);
 
%Display the same to the user
fprintf('x = %.2f\n',x)
fprintf('y = %.2f\n',y)
I have named my file as polarcartesian.m and have saved it on my local computer.

Explanation

We are using the input function in Matlab to get the value of angle in radians(See the solution section for why we are getting the value in radians). Then we are getting the value of ‘r’ using the input function. We are storing the values of angle in variable angle and value of ‘r’ in radians. We are using the elementary functions cos and sin to write the equations given in the question. Finally we are using fprintf function to display the value of x and y to the user.

Input/Output

Matlab polarcartesian - Convert polar coordinates to rectangular coordinates
Matlab polarcartesian - Convert polar coordinates to rectangular coordinates

Test Yourself

Try to write a program to convert from Cartesian coordinate system to polar coordinate system and send it to me or comment below.
If you still have any doubt even after reading the complete post or if you have found any mistake then please do comment below or contact me so that it will not only help you but also the community. You can contact me from here: Contact me
Comment the value of x and y you are getting for a given input in the comment box below.
Program in this post has been high lighted using hilite.me
Keywords: Polar to Cartesian, rectangular coordinates, polar coordinates, 
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