# How do you graph y=cos4x?

Sep 30, 2016

The period of the cosine wave y = cos kx = $\frac{2}{k} \pi$.

Here, for y = cos 4x, the period is $\frac{2 \pi}{4} = \frac{\pi}{2}$

Let us make a Table, with spacing $\frac{\pi}{16}$.

for one period $x \in \left[0 , \frac{\pi}{2}\right]$

$\left(x , y\right) : \left(0 , 1\right) \left(\frac{\pi}{16} , \frac{1}{\sqrt{2}}\right) \left(\frac{\pi}{8} , 0\right) , \left(\frac{3}{16} \pi , - \frac{1}{\sqrt{2}}\right) \left(\frac{\pi}{4} , - 1\right)$

$\left(\frac{5}{16} \pi , . - \frac{1}{\sqrt{2}}\right) \left(\frac{3}{8} \pi , 0\right) \left(\frac{7}{16} \pi , \frac{1}{\sqrt{2}}\right) \left(\frac{\pi}{2} , 1\right)$

The graph for this Table will show one full wave.

Foe successive periods, move this graph laterally ( in the x-

direction), through $\frac{\pi}{2} = 1.57$ units..