Find the Exact Value csc((5pi)/13)

Problem

csc((5*π)/13)

Solution

1. Identify the expression as the cosecant of the angle (5*π)/13 radians.

2. Recognize that (5*π)/13 is not one of the standard angles (like π/6 π/4 or π/3 for which exact values are typically memorized in basic trigonometry.

3. Determine if the value can be simplified further using standard trigonometric identities or radical forms. Since 13 is a prime number and not a power of 2 or related to Fermat primes in a way that allows for simple constructible polygons, the exact value is most accurately represented in its trigonometric form.

4. State the value in terms of the sine function if preferred, as csc(θ)=1/sin(θ)

Final Answer

csc((5*π)/13)=csc((5*π)/13)

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