Math Snap

STEP 1

1. We are asked to find the exact value of $\csc \frac{\pi}{6}$.
2. The cosecant function is the reciprocal of the sine function.
3. We need to use the known value of $\sin \frac{\pi}{6}$.

STEP 2

1. Recall the definition of the cosecant function.
2. Determine the value of $\sin \frac{\pi}{6}$.
3. Calculate $\csc \frac{\pi}{6}$ using the reciprocal relationship.

STEP 3

Recall the definition of the cosecant function:
$$\csc \theta = \frac{1}{\sin \theta}$$

STEP 4

Determine the value of $\sin \frac{\pi}{6}$:
The angle $\frac{\pi}{6}$ radians is equivalent to $30^\circ$. The sine of $30^\circ$ is known to be:
$$\sin \frac{\pi}{6} = \frac{1}{2}$$

Calculate $\csc \frac{\pi}{6}$ using the reciprocal relationship:
$$\csc \frac{\pi}{6} = \frac{1}{\sin \frac{\pi}{6}} = \frac{1}{\frac{1}{2}} = 2$$ The exact value of $\csc \frac{\pi}{6}$ is:
$$\boxed{2}$$