Question

MATLAB ONLY MATLAB ONLY

MATLAB ONLY MATLAB ONLY

(x(t), y(t)) (t - sint, 1- cost 1. (15 pts) Consider the parametrized curve 0,7] 2) (10pts) Calculate the length of (x(t), y(t)) from 0 to 7 1) (5pts) Plot the graph of parametrized curve on

Answer 1

clc
clear
close all

%% 1)
%defining x(t) and y(t) as anonymous functions
x = @(t) t - sin(t); y = @(t) 1 - cos(t);

% defining the time vector t [0 pi] with 100 points
t = linspace(0,pi,100);

% graphing the parametric curve for t = [0 pi]
plot(x(t),y(t))
xlabel('x(t)')
ylabel('y(t)')
grid on

%% 2)
% applying the general formula for arc length computation
dxdt = @(t) 1-cos(t); dydt = @(t) sin(t); %differentiating x and y w.r.t t
f = @(t) sqrt(dxdt(t).^2 + dydt(t).^2);% the general arc length function
Length = integral(f,0,pi) % arc length on t = [0 pi]

2 1.8 1.6 1.4 F 1.2 1 0.8 0.6 0.4 0.2 0 0 0.5 2 1 1.5 2.5 3 3.5 x(t) (1)A

Length 4.0000

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