Find the Exact Value csc((17pi)/6)

Problem

csc((17*π)/6)

Solution

1. Subtract multiples of 2*π to find the coterminal angle within the interval [0,2*π)

(17*π)/6−2*π=(17*π)/6−(12*π)/6

(17*π)/6−(12*π)/6=(5*π)/6

2. Apply the reciprocal identity for the cosecant function.

csc((5*π)/6)=1/sin((5*π)/6)

3. Determine the sine value for the angle in the second quadrant.

sin((5*π)/6)=sin(π−π/6)

sin((5*π)/6)=sin(π/6)

sin(π/6)=1/2

4. Calculate the reciprocal to find the final value.

csc((5*π)/6)=1/(1/2)

csc((5*π)/6)=2

Final Answer

csc((17*π)/6)=2

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