MHB Limit of Trigonometric Function....2

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The limit of csc(2x) as x approaches π/2 from the right side is debated, with one participant asserting the limit is positive infinity based on their graph. However, the textbook indicates the limit is negative infinity, prompting questions about the reasoning behind this conclusion. The discrepancy arises from the behavior of the sine function near π/2, where it approaches zero from the negative side, causing csc(2x) to diverge negatively. Clarification is sought on the correct interpretation of the limit and the graphing approach used. Understanding the function's behavior near critical points is essential for accurate limit evaluation.
nycmathdad
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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
 
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Problem 1.5.39.
Odd numbered.
Look up the answer and graph it.
 

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