Answer:
- vertical asymptote at π
- vertical asymptote at 2π
- goes through point (π/4, √2)
- goes through point (π/3, 2√3/3)
Step-by-step explanation:
See the attached graph.
__
The cosecant function is the reciprocal of the sine function, so it will have asymptotes where the sine function is zero: at multiples of π.
Since you have memorized the short table of trig functions, you know that ...
sin(π/4) = 1/√2 ⇒ csc(π/4) = √2
sin(π/3) = (√3)/2 ⇒ csc(π/3) = 2/√3 = (2√3)/3
