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

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Answer 1 · 2018-07-28T15:40:03

See graph and details.

#y = csc (pi - x ) = 1/sin ( pi - x ) = 1/sin x notin ( - 1, 1 )#

And, asymptotic x = any zero of the denominator #sin x#

# = kpi, k = 0, +-1, +-2, +-3, ...#

The period = period of #sin x = 2 pi #.

Graph for two periods,

#x in ( - 2 pi, 2 pi )#, with asymptotes #x = +- pi# and

y not-to-be-in #( -1, 1 )#:
graph{(y sin x - 1)(y^2-1)(x)(x^2-(pi)^2)(x^2-4(pi)^2)=0[-10 10 -5 5]}