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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.
$\endgroup$ 12 Answers
$\begingroup$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.
$\endgroup$ $\begingroup$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!
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