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. Simplify the angle by finding its coterminal equivalent within the interval [0,2*π)

(5*π)/2=2*π+π/2

4. Evaluate the sine of the coterminal angle.

sin((5*π)/2)=sin(π/2)

sin(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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