How do you graph $y = - csc (4 x - π)$ $y=-csc(4x-pi)$ and include two full periods?

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Answer 1 · 2018-07-17T05:47:20

$y = - csc (4 x - π) \in (- \infty, - 1] U [1, \infty)$ $y = - csc ( 4x - pi ) in ( - oo, -1] U [1, oo )$

Period = $\frac{2 π}{4} = \frac{π}{2}$ $(2pi)/4 = pi/2$ ;

Graph for two periods:: $x \in (\frac{π}{4}, \frac{5}{4} π)$ $x in ( pi/4, 5/4pi )$ ,

with asymptotes $x = \frac{π}{4}, \frac{3}{4} π$ $x = pi/4, 3/4pi$ :
graph{(y sin (4x - pi )+1)(x- pi/4+0y)(x-5/4pi+0y)=0 [pi/4 5/4pi -pi pi]}

See bounds $x = \frac{π}{2} = 1.57 and x = 4.71$ $x = pi/2 = 1.57 and x = 4.71$ .

How do you graph y=−csc(4x−π)y=-csc(4x-pi) and include two full periods?