Find the Exact Value csc(-(5pi)/2)

Problem

csc(−(5*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(−(5*π)/2)=1/sin(−(5*π)/2)

3. Find a coterminal angle by adding 2*π (or (4*π)/2 to the angle until it is within the standard interval [0,2*π)

−(5*π)/2+(4*π)/2=−π/2

−π/2+(4*π)/2=(3*π)/2

4. Evaluate the sine of the coterminal angle.

sin((3*π)/2)=−1

5. Calculate the final value by taking the reciprocal.

1/(−1)=−1

Final Answer

csc(−(5*π)/2)=−1

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