Page 35 -

[x,y]=pol2cart(th,rho);
plot(x,y)
axis equal

Example 1.17
Graph the polar plot of a spiral.

Solution: The equation of the spiral is given by:

r = aθ

Its polar plot can be viewed by executing the following script M-file (a = 3):

th=0:2*pi/100:2*pi;
rho=3*th;
polar(th,rho)

In-Class Exercises

Pb. 1.17 Prove that the polar equation r = 1 + ε cos(θ), where ε is always
between –1 and 1, results in an ellipse. (Hint: Relate ε to the ratio between the
semi-major and semi-minor axis.) It is worth noting that the planetary orbits
are usually described in this manner in most astronomy books.
Pb. 1.18 Plot the three curves described by the following polar equations:

r =−22sin( ),θ r = −1 2 sin( ),θ r = 2 sin( 2 )θ

Pb. 1.19 Plot:

r = sin(2θ) cos(2θ)

The above gives a flower-type curve with eight petals. How would you make
a flower with 16 petals?
Pb. 1.20 Plot:

r = sin (θ)
2

This two-lobed structure shows the power distribution of a simple dipole
antenna. Note the directed nature of the radiation. Can you increase the
directivity further?

© 2001 by CRC Press LLC