Return the max, min, and zeros of a function y, and plot it., R

Return the max, min, and zeros of a function y, and plot it.

#R version 3.3.2
# Return the max, min, and zeros of a function y, and plot same.
library(ggplot2)
# Define some constants first
pi=3.1416
b=(2*pi)/365.2422
c=-79.5*b
# y is the solar declination function f(d) where d is the day of year
d=seq(0,365,1)
y=23.4368*sin((b*d)+c)
cat("The max. of y is", max(y), "and occurs at index x =", which.max(y), "\n")
cat("The min. of y is", min(y), "and occurs at index x =", which.min(y), "\n")
# Search the function output vector y for zeros and return exact zero(s), or 
#   a pair of adjacent values between which a zero exists.
cat("Searching for the zero points in vector y...\n")
for(i in 2:length(y)) { 
  test=abs(sign(y[i-1])+sign(y[i]));
  if(test==0) { cat("x.indexes",i-1,i,"y.values",y[i-1],y[i],"\n") };
  if(test==1 && y[i]==0) { cat("x.index",i,"y.value",y[i],"\n") }; 
}
# Now plot the function
title1="Solar Declination by Day of Year"
qplot(d,y,geom="path",main=title1,xlab="Day of Year",ylab="Solar Declination")+
scale_x_continuous(breaks=seq(0,365,73))+scale_y_continuous(breaks=seq(-25,25,5))+
geom_line(aes(x=80.5,y=y),color="green")+geom_line(aes(x=263,y=y),color="orange")+
geom_line(aes(x=172,y=y),color="yellow")+geom_line(aes(x=354,y=y),color="blue")+
annotate("text",x=c(36,126,217,308),y=-5,label=c("Winter","Spring","Summer","Fall"))
# Done.


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