Question Sheet 2 - Challenge Problem

Often, despite understanding the individual parts of a problem, solving the problem as a whole can be challenging. It is therefore important to develop a range of techniques to deal with difficulties when they arise. One approach that can often be helpful is breaking a problem back down into pieces we understand. 

Suppose a student is trying to plot 2 functions using the plot function, namely, sin(x) and ((cos(x))/(2x)). However, when they evaluate the command, they get an error message as displayed below:

Plot[sin(x),cos(x)/2*x,{0,2π}]

1. What is the form of the plot command when you want plot to functions on the same graph? Does this match the above code or not? If not, make any relevant changes.

2. How do you write a trigonometric function in Mathematica? Does this match the above function or not? If not, make any relevant changes.

3. At this point you should have an output similar to that shown below:

It is tempting to assume that since Mathematica has given us an output that ‘works’, i.e. has given us a graph, that we have plotted our function correctly. We should however do some ‘sense-making’ checks. What is the value of sin(x) and ((cos(x))/(2x)) at 0? Does this match our graph or not? If not, why might this be? Make any relevant alterations to the code and plot below.