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Select your answer Simplify \( \csc \left(\frac{5 \pi}{6}\right) \) \( -\quad-\infty \) 0 2

Ask by Gibson Ward. in the United States
Feb 28,2025

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The simplified value of \( \csc\left(\frac{5\pi}{6}\right) \) is 2.

Solución

To simplify csc(5π/6), recall that csc(θ) = 1/sin(θ). Step 1: Evaluate sin(5π/6). We have sin(π - θ) = sin(θ), so sin(5π/6) = sin(π/6) = 1/2. Step 2: Compute csc(5π/6) = 1/(1/2) = 2. Thus, the simplified value is 2.

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The value of \( \csc \left(\frac{5 \pi}{6}\right) \) simplifies to \( \frac{1}{\sin \left(\frac{5 \pi}{6}\right)} \). Since \( \sin \left(\frac{5 \pi}{6}\right) = \frac{1}{2} \), it follows that \( \csc \left(\frac{5 \pi}{6}\right) = \frac{1}{\frac{1}{2}} = 2 \). So, the correct answer is 2!

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