Graph the following polar coordinates 2pi6 311pi6 Graph the

Graph the following polar coordinates: (-2,pi/6) (3,-11pi/6) Graph the set of points whose polar coordinates satisfy the given conditions: 2 r 3 : 2pi/3 theta 5pi/6 Convert the Cartesian equation into an equivalent polar equation: x2 + (y - 3)2 = 9 Find an equivalent Cartesian equation and describe the graph: r cos theta + r sin theta = 1 Sketch the graph of the polar equation: r = 2 + 4 sin theta . [ you need to show your complete work ! ]

Solution

here are the matlab codes :-
(a.)r1=-2;
r2=3;
theta1=pi/6;
theta2=-11*pi/6;
x1=r1*cos(theta1);
y1=r1*sin(theta1);
x2=r2*cos(theta2);
y2=r2*sin(theta2);

X=[x1,x2];
Y=[y1,y2];
plot(X,Y,\'h\');
grid on;


(b.)
r=linspace(2,3,1000);
theta=linspace(2*pi/3,5*pi/6,1000);
x=r.*cos(theta);
y=r.*sin(theta);
plot(x,y);


(c.)x=r*cos()

y-3=r*sin()

where r=3;

so (x,y)=(3 *cos,3+3*sin)

(d.)matlab code

theta=linspace(0,2*pi,1000);
r=2+4*sin(theta);

x=r.*cos(theta);
y=r.*sin(theta);

plot(x,y)

(b.)

(d.)