In Blog 22, let’s see how to create mathematical expressions for your graph.
Mathematical expressions on graphs are made possible through expression(paste()) and substitute(). If you need mathematical expressions as axis labels, switch off the default axes and include Greek symbols by writing them out in English. You can create fractions through the frac() command. Note how we obtain the plus or minus sign through the syntax: %+-%
Here is a nice example. Let’s create a set of 71 values from – 6 to + 6. These values are the horizontal axis values.
x <- seq(-6, 6, len = 71)
Now we plot a cosine function using a continuous curve (using type="l") while suppressing the x axis using the syntax: xaxt="n"
plot(x, cos(x),type="l",xaxt="n", xlab=expression(paste("Angle ",theta)), ylab=expression("sin "*beta))
where we have inserted relevant mathematical text for the axis labels using expression(paste()). Here is the graph so far:

Now we create a horizontal axis to our own specifications, including relevant labels:
axis(1, at = c(-2*pi, -1.5*pi, -pi, -pi/2, 0, pi/2, pi, 1.5*pi, 2*pi), lab = expression(-2*phi, -1.5*phi, -phi, -phi/2, 0, phi/2, phi, 2*phi, 1.5*phi))

Let’s put in some mathematical expressions, centred appropriately. The first argument within each text() function gives the value along the horizontal axis about which the text will be centred.
text(-0.7*pi,0.5,substitute(chi^2=="23.5"))
text(0.1*pi, -0.5, expression(paste(frac(alpha*omega, sigma*phi*sqrt(2*pi)), " ", e^{frac(-(5*x+2*mu)^3, 5*sigma^3)})))
text(0.3*pi,0,expression(hat(z) %+-% frac(se, alpha)))
Here is our graph, complete with mathematical expressions:

That wasn’t so hard! In Blog 23 we will look at further plotting techniques in R.
See you later!
David

Annex: R codes used

[code lang="r"]
# Create a set of 71 horizontal axis values.
x <- seq(-6, 6, len = 71)

# Plot a cosine function.
plot(x, cos(x),type="l",xaxt="n", xlab=expression(paste("Angle ",theta)), ylab=expression("sin "*beta))

# Custimise a horizontal axis.
axis(1, at = c(-2*pi, -1.5*pi, -pi, -pi/2, 0, pi/2, pi, 1.5*pi, 2*pi), lab = expression(-2*phi, -1.5*phi, -phi, -phi/2, 0, phi/2, phi, 2*phi, 1.5*phi))

# Add a few mathematical expressions.
text(-0.7*pi,0.5,substitute(chi^2=="23.5"))
text(0.1*pi, -0.5, expression(paste(frac(alpha*omega, sigma*phi*sqrt(2*pi)), " ", e^{frac(-(5*x+2*mu)^3, 5*sigma^3)})))
text(0.3*pi,0,expression(hat(z) %+-% frac(se, alpha)))
[/code]