# 媒介変数 t
t<-seq(-pi,pi,length=100)
X<- 10*cos(t)
Y<- 5*sin(t)
plot(X, Y, type="l",col="red",lwd = 1,xlim=c(-10,10),ylim=c(-10,10))
par(new=T)
X<- 5*cos(t)
Y<- 10*sin(t)
plot(X, Y, type="l",col="blue",lwd = 1,xlim=c(-10,10),ylim=c(-10,10))
title("Ellipse ")

dev.new()
t<-seq(-2*pi,2*pi,length=100)
X<- t-sin(t)
Y<- 1-cos(t)
plot(X, Y, type="l",col="red",lwd = 1,xlim=c(-10,10),ylim=c(-10,10))
par(new=T)
 a=1;b=6;
X<- a*t-b*sin(t)
Y<- a-b*cos(t)
plot(X, Y, type="l",col="blue",lwd = 1,xlim=c(-10,10),ylim=c(-10,10))
abline(h=0,col=8)
mtext("a= b= 1  (Cycloid)",3,0,col=2)
mtext(paste(" a= ",a,"   b= ",b),3,0.6,col=4)
title("Trochoid")


dev.new()
t<-seq(-pi,pi,length=100)
X<- 5*(cos(t))^2
Y<- 5*(sin(t))^2
plot(X, Y, type="l",col=2,lwd = 1,xlim=c(-6,6),ylim=c(-6,6))

par(new=T)
X<- 5*(cos(t))^3
Y<- 5*(sin(t))^3
plot(X, Y, type="l",col=3,lwd = 1,xlim=c(-6,6),ylim=c(-6,6))

par(new=T)
X<- 5*(cos(t))^4
Y<- 5*(sin(t))^4
plot(X, Y, type="l",col=4,lwd = 1,xlim=c(-6,6),ylim=c(-6,6))

par(new=T)
X<- 5*(cos(t))^5
Y<- 5*(sin(t))^5
plot(X, Y, type="l",col=5,lwd = 1,xlim=c(-6,6),ylim=c(-6,6))
mtext("n = 2, 3, 4, 5",3,0)
title(" Asteroid")
　
dev.new()
#polar
 r<-2*sin(2*t)
X<- r*cos(t)
Y<- r*sin(t)
plot(X, Y, type="l",col="blue",lwd = 1,xlim=c(-2,2),ylim=c(-2,2))
par(new=T)
r<-2*cos(3*t)
X<- r*cos(t)
Y<- r*sin(t)
plot(X, Y, type="l",col="red",lwd = 1,xlim=c(-2,2),ylim=c(-2,2))
text(-1,2,"r=2sin(2t)"　,col="blue")
text(1,2,"r=2cos(3t)"　,col="red")
title("Leaves ")


dev.new()
 r<-cos(t)+1
X<- r*cos(t)-1
Y<- r*sin(t)
plot(X, Y, type="l",col="red",lwd = 1,xlim=c(-2,2),ylim=c(-2,2))

par(new=T)
 r<-2*cos(t)-1
X<- r*cos(t)-1
Y<- r*sin(t)
plot(X, Y, type="l",col="blue",lwd = 1,xlim=c(-2,2),ylim=c(-2,2))
text(-1,2,"r=2cos(t)+1"　,col="blue")
text(1,2,"r=cos(t)-1"　,col="red")
title("Cardioid ")