Find the Exact Value csc(3)

Problem

csc(3)

Solution

1. Identify the expression as the cosecant of 3 radians.

2. Recognize that 3 is not a standard reference angle (like π/6 π/4 or π/3 for which exact values are typically expressed using radicals or integers.

3. Apply the reciprocal identity for cosecant, which states that csc(θ)=1/sin(θ)

4. Determine that since 3 is not a multiple of π the value is a transcendental number that cannot be simplified further into a more "exact" algebraic form.

Final Answer

csc(3)=1/sin(3)

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