Question

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

Answer 1

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]}