# How to plot the graph of f(x)= 10 cos 3x?

Jul 1, 2015

Your function is a cosine function with amplitude $10$ and period $\frac{2}{3} \pi$.

#### Explanation:

The graph of your function is the same as the one from a "normal" cosine BUT:
1] Amplitude will be $10$;
2] Period will be: $p e r i o d = \frac{2 \pi}{\textcolor{red}{3}}$ using the $3$ in front of the $x$ in the argument of your $\cos$. This means that your $\cos$ is "squeezed", completing an entire oscillation between $0$ and $\frac{2}{3} \pi$ instead of between $0$ and $2 \pi$!

Graphically:
$y = f \left(x\right) = 10 \cos \left(3 x\right)$
graph{10(cos(3x)) [-28.88, 28.86, -14.43, 14.45]}

Where you can see the outline of a normal $\cos$ function but with amplitude of $10$ and period $\frac{2}{3} \pi = 2.09 r a d$

I add another plot, easier to "see" (I hope!):