Evaluate csc((3pi)/2)

Problem

csc((3*π)/2)

Solution

1. Identify the definition of the cosecant function in terms of the sine function.

csc(θ)=1/sin(θ)

2. Substitute the given angle into the identity.

csc((3*π)/2)=1/sin((3*π)/2)

3. Determine the value of the sine function at the angle (3*π)/2 using the unit circle.

sin((3*π)/2)=−1

4. Simplify the expression by dividing the numerator by the result from the previous step.

1/(−1)=−1

Final Answer

csc((3*π)/2)=−1

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