Problem

Find csc⁡(2π). Enter " U " if it is undefined.

Answer

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Answer

Final Answer: U

Steps

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

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

Step 3 ：Therefore, csc⁡(2π)=1sin⁡(2π)=10.

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

Step 5 ：Final Answer: U

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