Why does csc(2x) approach negative infinity as x approaches π/2 from the right?

[nycmathdad]

Find the limit of csc(2x) as x tends to pi/2 from the right side.

I decided to graph the function. Based on the graph, I stated the answer to be positive infinity.
According to the textbook, the answer is negative infinity. Why is negative infinity the right answer?

Thanks

 

[jonah1]

Problem 1.5.39.
Odd numbered.
Look up the answer and graph it.