How to sketch a sinc function by hand?

Question

I have to do this for an upcoming exam, but cannot find anywhere (in the textbook or online) how to do this.

I only really need to know a couple points to plot it... when x = 0, and then the earliest crossing of the x-axis.

Answer 1

You know the value at zero, it goes to zero at $x = n \pi$ and in-between reaches the maximum and minimum at close to $x = (n+ \frac{1}{2}) \pi$ (when $n>0$ or $n<-1$) with the value at these points being $\frac{(-1)^n}{(n+ \frac{1}{2}) \pi}$. So knowing these you should be able to roughly sketch the function.

Answer 2

http://www.wolframalpha.com/input/?i=plot+sinc%28x%29

Answer 3

I think its helpful also to graph it with $\frac{1}{x}$

http://www.wolframalpha.com/input/?i=plot+sinc%28x%29%2C+1%2Fx

If you write the function as $f(x) = \frac{\sin(x)}{x}$ for $x \not=0$ and $1$ if $x=0$ you can see that it will be zero at exactly when $\sin(x)$ is zero (except at $0$ where it is $1$).