How do you graph $y = 2 cot 4 x$ $y=2cot4x$ ?

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How do you graph $y = 2 cot 4 x$ $y=2cot4x$ ?

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Answer 1 · 2017-10-07T07:40:06

$↓ ↓ ↓ ↓$ $darr darr darr darr$

Explanation:

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

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

$a = 2$ $a=2$

$b = 4$ $b=4$

$c = 0$ $c=0$

$d = 0$ $d=0$

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

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

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

$2 .$ $2.$ Now graph

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

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

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

Three points are $\to (\frac{π}{16}, 2), (\frac{π}{8}, 0), (\frac{3 π}{16}, - 2)$ $-> (pi/16,2), (pi/8,0), ((3pi)/16,-2)$

Therefore, $y = 2 cot 4 x \to$ $y=2cot4x->$
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How do you graph $y = 2 cot 4 x$ $y=2cot4x$ ?

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