Question

 Write your answer code into one function file on matlab

 The spiral of Archimedes. The spiral of Archimedes is a curve described in polar coordinates by the equation

 r= kθ

 Where r is the distance of a point from the origin, and d is the angle of that point in radians with respect to the origin.

 Write a function file to compute the spiral of Archimedes with varying number of inputs (no input, one input, two inputs) for k, 0 and varying number of outputs (no output, one output, two outputs, which are r and

 computation time spent on computing r within [for .. end] loop). Default values of the two input arguments are: 0 ≤ θ ≤ 15π, k = 0.25.

Answer 1

function varargout = ArchimedesSpiral(varargin)
if isempty(varargin)
k=.025;
theta=linspace(0,15*pi,10000);
elseif length(varargin)==1
k=varargin{1};
theta=linspace(0,15*pi,10000);%2nd argument is theta
else
k=varargin{1};
theta=varargin{2};
end
tic
for i=1:length(theta)
r(i)=k*theta(i);
end
timeRequired=toc;
if nargout==1
varargout{1}=r;
elseif nargout==2
varargout{1}=r;
varargout{2}=timeRequired;
end

Command Window >> ArchimedesSpiral(.1,0:.01:2*pi) >> [r]=ArchimedesSpiral(.1,0:1:10) 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 0 0.1000 0.2000 0.3000 >> [r, t]-ArchimedesSpiral(.1,0:1:10) 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.80000.9000 1.0000 4.6700e-05 >> [r, t]=ArchimedesSpiral; t = 0.0037 >> [r, t]=ArchimedesSpiral (34); >> t t = 0.0023