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)` |
---|---|---|

0.01 | 0.01 | 100 |

0.5 | 0.48 | 2.09 |

`pi/2` | 1 | 1 |

2 | 0.91 | 1.10 |

3 | 0.14 | 7.09 |

3.1 | 0.04 | 24.05 |

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*.