trigonometric function r=sin(4*theta)
theta=seq(0,2*pi,length=1000)
r=sin(4*theta)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=4+3*sin(theta)
theta=seq(0,2*pi,length=1000)
r=4+3*sin(theta)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=1+sin(theta)
theta=seq(0,2*pi,length=1000)
r=1+sin(theta)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=cos(2*theta)
theta=seq(0,2*pi,length=1000)
r=cos(2*theta)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=sin(8*theta/5)
theta=seq(0,10*pi,length=1000)
r=sin(8*theta/5)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=theta^2
theta=seq(0,16*pi,length=1000)
r=theta^2
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=cos(theta/3)
theta=seq(0,2*pi,length=1000)
r=cos(theta/3)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=1+2*cos(theta)
theta=seq(0,2*pi,length=1000)
r=1+2*cos(theta)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=2+sin(3*theta)
theta=seq(0,2*pi,length=1000)
r=2+sin(3*theta)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")

trigonometric function r=1+2sin(3*theta)
theta=seq(0,2*pi,length=1000)
r=1+2*sin(3*theta)
x=r*cos(theta)
y=r*sin(theta)
plot(x,y, type="l")
