Draw the graph of $y=\frac{1}{3}\cos(x)$

Question

How can I draw the graph of $y=\frac{1}{3}\cos(x)$ with the point along $x$-axis are $0,\pm\frac{\pi}{2},\pm\pi,\pm\frac{3\pi}{2},\dots$. Also show the corresponding points along $y$-axis.

Answer 1

The graph will be similar to the graph of $y=\cos(x)$ but compressed along the $y$ axis by the factor $1/3$.

You can generate a very similar graph on WolframAlpha.

Answer 2

Some hints:

• $f(x) = \cos{x}$ is an even function.
• $f(x)$ is bounded: $-1 \leq f(x) \leq 1$.
• $f(x)$ is a $2 \pi$ periodic function, so $f(x+2\pi) = f(x)$.
• $f(0) = 1, \ f(\pi/2) = 0, \ f(\pi) = -1, \ f(3\pi/2) = 0.$

This is trying to tell us that you just need to draw the graph of $f(x)$ when $x\in [0,2\pi]$, scale it down three times ($y = f(x)/3$) and do a mirror reflection with respect to the $y$ axis in order to get the points $y = y(x)$ for $x<0$.

I'm shure you can take it from here.

Cheers!