Find the Exact Value csc(-pi/2)

Problem

csc(−π/2)

Solution

1. Identify the reciprocal relationship for the cosecant function.

csc(θ)=1/sin(θ)

2. Substitute the given angle into the reciprocal identity.

csc(−π/2)=1/sin(−π/2)

3. Apply the odd function property of the sine function, sin(−x)=−sin(x)

sin(−π/2)=−sin(π/2)

4. Evaluate the sine of the reference angle.

sin(π/2)=1

5. Calculate the final value by substituting the sine value back into the fraction.

csc(−π/2)=1/(−1)

Final Answer

csc(−π/2)=−1

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