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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