How do you sketch one cycle of #y=cscx#?

1 Answer
Feb 27, 2017

Answer:

Like a #sin# graph, but opposite.

Explanation:

#csc(x)=1/sin(x)#

Sketch a #sin# graph, then draw loops down to meet each maximum or minimum point.

graph{csc(x) [-10, 10, -5, 5]}

Notice that at each stationary point on this graph, there would usually be a stationary point for #sin(x)#.

Each time the #sin# graph would approach #0#, the #csc# graph will approach #oo# or #-oo#. Each time the #sin# graph approaches #+-1#, the #csc# graph approaches #+-1#.

These are because

#csc(x)=1/sin(x)#

#sin(x)=0 -> csc(x) = 1/0 = oo#
#sin(x)=1 -> csc(x) = 1/1 = 1#