Question

How do you draw the graph of `y=-1-cscx` for `0<=x<2pi`?

Answer 1

Explanation:

Think of it this way, csc(x) is an endless repeating funtion like that in black (I graphed it for you so you can see). When you are asked to shade a region or to find the region that is between `0` and `2pi` all

• First is check to see if the limits are included or not, in this case we have the `0` which is included bcause it is the `x` bigger than or equal to (whenever there is equal to it is included and has a solid line on the graph and means that point is considered a part of the bound). Notice the `2pi` is not included and is therefore a dashed line.
• Then I'm assuming you know that you label the x-axis `0, pi, (3pi)/2 and 2pi` which is just another way of looking at the same thing the unit circle shows. That is just one whole cycle of the function.

By the way if you weren't sure of the actual function how it looks you can just plot points and connect them. Just like `sin(x)` and `cos(x)` you should know `csc(x)` graph has the continuous curves.