# How do you graph y=2cot4x?

Oct 7, 2017

$\downarrow \downarrow \downarrow \downarrow$

#### Explanation:

$1.$ Find the period, phase shift, & vertical shift

Using $a \cdot \cot \left(b x + c\right) + d$,
where:

• $a = 2$
• $b = 4$
• $c = 0$
• $d = 0$

Period $= \frac{\pi}{b} = \frac{\pi}{4}$... One cycle completes at $\frac{\pi}{4}$

Phase shift $= \frac{c}{b} = \frac{0}{4} = 0$...Phew! that means no problem

Vertical shift $= d = 0$... Again no problem!

$2.$ Now graph

At $\frac{\pi}{8}$, (half of the period), $y = 0$

At $\frac{\pi}{16}$, (half of the $\frac{\pi}{8}$), $y = a = 2$

At $\frac{3 \pi}{16}$, (batween $\frac{\pi}{8}$ and the period), $y = - a = - 2$

Three points are $\to \left(\frac{\pi}{16} , 2\right) , \left(\frac{\pi}{8} , 0\right) , \left(\frac{3 \pi}{16} , - 2\right)$

Therefore, $y = 2 \cot 4 x \to$