How do you graph y=csc(x+(5pi)/6)+4?

1 Answer
A. S. Adikesavan
Aug 3, 2018

See graph and explanation.

Explanation:

Value of csc X notin ( -1, 1 ) and

X ne asymptotic kpi, k = 0, +- 1, +-2, +-3, ...

Here,

y = csc ( x + 5/6pi ) + 4 notin { - 1 + 4, 1 + 4 ) = ( 3, 5 ) and

x + 5/6pi ne asymptotic kpi rArr x ne asymptotic ( k - 5/6)pi .

So, x ne ...-17/6 pi, -11/6 pi, - 5/6 pi, 1/6 pi, 7/6 pi, 13/6 pi, ...

Period = 2pi.

Vertical shift = 4.

Phase shift = - 5/6 pi.

Axis of the graph: y = 3.

See graph, depicting all these aspects. Slide the graph uarr larr darr rarr, to see around.
graph{((y-4) sin ( x + 5/6 pi )-1 )(y-3+0x)(y-4+0x)(y-5+0x)(x+11/6pi+0.0001y)(x+5/6pi+0.0001y)(x-1/6pi+0.0001y)(x-7/6pi+0.0001y)=0[-8pi 8pi 0 8pi]}

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