R Lesson 34: Let’s Plot Some Trigonometric Functions

Hello everybody,

Michael here, and in the last two posts we discussed the basics of trigonometry-both with R and basic trig in general. This time, we’ll explore how to plot the three basic trigonometric functions with R-sine, cosine and tangent!

A basic R sine plot

To start our lesson, we’ll create a basic R plot of a sine function. Here’s the code we’ll utilize to create our basic R sine plot:

> x <- seq(0,7*pi,length.out=100)
> y <- sin(x)
> plot(x, y, type='l')

As you can see, these three lines of R code gave us a very simple R sine plot. How did the code accomplish this graph creation? Let’s explain!

• The seq() function used for the x variable takes 3 parameters-a starting point for the sequence (0), an ending point for the sequence (7*pi), and a value for length.out which indicates how many equally spaced values you want in the sequence (I opted for 100 in this case). The sequence itself will be represented on the x-axis
• The y variable takes the sine of all 100 values genereated from the sequence in the x variable-these sine values are then plotted on the y-axis.
• The plot() function takes both the x and y variables along with a type parameter, which indicates the style of graph you want to plot. In this case, I set type to l, indicating I want to plot the sine function with a [solid] linear style.

Now, what exactly does 7*pi mean here? In this case, it indicates that the sequence will end at 7*pi, or roughly 21.98. Something else to note whenever you use pi in trigonometric function plots-sine functions have these things called periods, which in plain English represent the point in a function where it repeats its values. Sine functions have a period of 2*pi which means that they repeat their values every 2*pi-or 6.28-units. Since the endpoint of this sequence is 7*pi, there are 3 1/2 periods in this graph as shown by the 3 1/2 low and high points on this graph.

A basic R cosine plot

Now that we’ve explored sine plots with R, let’s turn our attention to cosine plots! Here’s the code to create a basic cosine plot in R:

> x <- seq(0, 10*pi, length.out=100)
> y <- cos(x)
> plot(x, y, type='l')

Conceptually, the cosine plot works the same way as the sine plot, as both plots have periods of 2*pi (represented by the peaks and valleys in this graph). Since the endpoint of the sequence is 10*pi, this cosine plot will have five periods. Both plots will also generate a sequence of X equally spaced values (X being the number specified in the length.out parameter).

The one difference between the cosine and sine plots? The former calculates out the cosine for all sequence values while the latter calculates the sine for all sequence values.

Last but not least, let’s explore tangent plots!

A basic R tangent plot:

Just as we explored basic R sine and cosine plots, let’s explore how to create a basic R tangent plot! Here’s the code for one such plot:

> x <- seq(-5*pi, 3*pi, length.out=100)
> y <- tan(x)
> plot(x, y, type='l')

Creating the tangent plot follows the same logic as creating the sine and cosine plots, with the exception that you’re looking for the tangent of all the equally spaced values in the sequence.

You may also be wondering why the tangent plot looks so different from the sine and cosine plots. One main reason for this is because tangent functions, unlike sine and cosine functions, has a little something called asymptotes.

What are asymptotes? To explain this concept, I feel it is important to mention that sine and cosine functions have a range of values between -1 and 1, which explains why we get smooth, wave-like plots as shown earlier in this post. However, tangent functions have a range of values between negative infinity and positive infinity. Asymptotes are straight imaginary lines that approach various curves on the tangent plot but never fully meet them.

Still a little confused? Allow me to illustrate:

This is the tangent plot we just created. Pay attention to the two curves on this graph with the red line borders (aka the asymptotes). The asymptotes on the first curve (the one that appears to have its lowest point at -60 on the y-axis) appears to be going down to negative infinity, yet the asymptotes will never touch the curve no matter how far down it goes. Likewise for the second curve (the one that appears to have its highest point at 60), which appears to be going up to positive infinity but similar to the first curve, the asymptotes will never touch the curve no matter how high it goes.

Thanks for reading,

Michael