How do you sketch one cycle of y=cscx?

1 Answer
reudhreghs
Feb 27, 2017

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

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