Find the Exact Value csc((9pi)/2)

Problem

csc((9*π)/2)

Solution

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

2. Divide the numerator by the denominator to express the fraction as a mixed number.

(9*π)/2=4*π+π/2

3. Subtract multiples of 2*π since the cosecant function has a period of 2*π

(9*π)/2−2*(2*π)=π/2

4. Apply the reciprocal identity for cosecant.

csc(π/2)=1/sin(π/2)

5. Evaluate the sine of the simplified angle.

sin(π/2)=1

6. Calculate the final value.

1/1=1

Final Answer

csc((9*π)/2)=1

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