(Solved Homework): a. Polar Plots Butterfly Curve rho = cos(50) + sin(3 theta) + 0.3 Flower Curve rho = sin(2 theta)cos(2 theta) polarplot(…

MATLAB

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a. Polar Plots Butterfly Curve rho = cos(50) + sin(3 theta) + 0.3 Flower Curve rho = sin(2 theta)cos(2 theta) polarplot() plots a line in polar coordinates, with theta indicating the angle in radians and rho indicating the radius value for each point. pol2cart()transforms corresponding elements of the polar coordinate arrays theta and rho to two- dimensional Cartesian, or xy, coordinates. Sketch the polar graphs on the interval [0, 2pi] for theta and using both functions. Use enough points so that your plot has a “smooth” appearance. Label the horizontal and vertical axes appropriately and provide a title. b. 3D Line Plot an hourglass shape using plot3() as shown in the figure.

Expert Answer

( a ) Matlab Code

theta = linspace(0, 2*pi, 500);

butterfly_curve = (cos(5*theta)).^2 + sin(3*theta) + 0.3;
curve1 = pol2cart(theta, butterfly_curve);
figure
p1 = polarplot(theta, curve1);
p1 = gca;
p1.ThetaColor = ‘black’;
p1.ThetaAxisUnits = ‘radians’;
p1.LineWidth = 2;
p1.GridColor = ‘red’;
title(‘Butterfly Curve’)
thetaticks(0:45:360);

Flower_curve = sin(2*theta) + cos(2*theta) ;
curve2 = pol2cart(theta, Flower_curve);
figure
p2 = polarplot(theta, curve2);
p2 = gca;
p2.ThetaColor = ‘red’;
p2.ThetaAxisUnits = ‘radians’;
p2.LineWidth = 2;
p2.GridColor = ‘red’;
title(‘Flower Curve’)
thetaticks(0:45:360);

OUTPUT

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