We recall that
`csc x=1/(sin x)`
So we will have asymptotes where `sin x` has value zero, that is:
x = ..., -3π, -2π, -π, 0, π, 2π, 3π, 4π, ...
We draw the graph of y = sin x first:
Graph of `y=sin x`.
Next, we consider the reciprocals of all the y-values in the above graph (similar to what we did with the y = sec x table we created above).
|`x`||`y` `= sin x`||`csc x` `= 1/(sin x)`|
I chose values close to `0` and `pi`, and some values in between. The pattern will be similar for the region from `pi` to `2pi` except it will be on the negative side of the axis.
We continue on both sides and realise the pattern will repeat. Now for the graph of y = csc x:
Graph of y = csc x.