MaplePolarExample1.mws

Polar Example 1

Picture and Computations

>    with(plots): 

Warning, the name changecoords has been redefined

>    polarplot(3-2*sin(theta),theta=0..2*Pi,thickness=3,numpoints=100,scaling=constrained);

>   

[Maple Plot]

>    Area:=Int((3-2*sin(theta))^2/2,theta=0..2*Pi);

Area := Int(1/2*(3-2*sin(theta))^2,theta = 0 .. 2*Pi)

>    value(%);

11*Pi

>    Perimeter:=Int(sqrt((3-2*sin(theta))^2+(2*cos(theta))^2),theta=0..2*Pi);

Perimeter := Int(((3-2*sin(theta))^2+4*cos(theta)^2)^(1/2),theta = 0 .. 2*Pi)

>    value(%);

20*EllipticE(2/5*6^(1/2))

>    evalf(%);

21.01004454

>    Perimeter:=Int(sqrt(13-12*sin(theta)),theta=0..2*Pi);

Perimeter := Int((13-12*sin(theta))^(1/2),theta = 0 .. 2*Pi)

>    value(%);

20*EllipticE(2/5*6^(1/2))

>