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

1 Answer
Aug 3, 2018

Answer:

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]}