Problem

Find $\csc (2 \pi)$. Enter " $U$ " if it is undefined.

Answer

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Answer

Final Answer: \(\boxed{U}\)

Steps

Step 1 ：The cosecant function, denoted as \(\csc(x)\), is defined as the reciprocal of the sine function, i.e., \(\csc(x) = \frac{1}{\sin(x)}\). Therefore, to find \(\csc(2\pi)\), we first need to find the value of \(\sin(2\pi)\).

Step 2 ：The sine function has a period of \(2\pi\), which means that \(\sin(2\pi) = \sin(0)\). We know that \(\sin(0) = 0\).

Step 3 ：Therefore, \(\csc(2\pi) = \frac{1}{\sin(2\pi)} = \frac{1}{0}\).

Step 4 ：However, division by zero is undefined in mathematics. Therefore, \(\csc(2\pi)\) is undefined.

Step 5 ：Final Answer: \(\boxed{U}\)

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