Questions: Find the exact value of csc (π/6).

Transcript text: Find the exact value of $\csc \left(\frac{\pi}{6}\right)$.

Solution

Solution Steps

Step 1: Calculate $\sin\left(\frac{\pi}{6}\right)$

The sine of $\frac{\pi}{6}$ is a well-known trigonometric value. We have: \[ \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \]

Step 2: Calculate $\csc\left(\frac{\pi}{6}\right)$

The cosecant function is the reciprocal of the sine function. Therefore, we calculate: \[ \csc\left(\frac{\pi}{6}\right) = \frac{1}{\sin\left(\frac{\pi}{6}\right)} = \frac{1}{\frac{1}{2}} = 2 \]

Final Answer

The exact value of $\csc\left(\frac{\pi}{6}\right)$ is $\boxed{2}$.

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