Find the Exact Value csc((13pi)/6)

Problem

csc((13*π)/6)

Solution

1. Identify the coterminal angle within the standard interval [0,2*π] by subtracting 2*π from the given angle.

(13*π)/6−2*π=(13*π)/6−(12*π)/6

(13*π)/6−(12*π)/6=π/6

2. Apply the definition of the cosecant function, which is the reciprocal of the sine function.

csc(π/6)=1/sin(π/6)

3. Substitute the known trigonometric value for sin(π/6) which is 1/2

csc(π/6)=1/(1/2)

4. Simplify the fraction to find the final value.

1/(1/2)=2

Final Answer

csc((13*π)/6)=2

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