 # Cycloid Curves and Parametric Equations

## Transcribed Text

The length of a curve given by a parametric equation x(t), y(t) is given by: Z b a p [x 0 (t)]2 + [y 0 (t)]2dt The cycloid curve is given by x = R(t−sin t), and y = R(1−cost). Determine the length of a cycloid with R = 8in for 0 ≤ t ≤ 2π.

## Solution Preview

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%This is the driver srcript.

% This piece is a test. The answer should be close to 64.
N=1000; %Number of integration points

times=linspace(0,2*pi,N);
dt=times(2)-times(1);

%parametrization of the cycloid
x=R*(times-cos(times));
y=R*(1-sin(times));

%numerical calculation of derivatives
dx_dt=diff(x)/dt;
dy_dt=diff(y)/dt;...
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