To convert an angle from degrees to radians, we use the fundamental relationship between the two units: a full circle is equivalent to 360 degrees, which is also equal to $2\pi$ radians.

Convert 30 Degrees to Radians

We know that:

• $180^\circ = \pi \text{ radians}$

From this, we can find the conversion factor for 1 degree:

• $1^\circ = \frac{\pi}{180} \text{ radians}$

To convert any angle from degrees to radians, we multiply the angle in degrees by the conversion factor $\frac{\pi}{180}$.

Calculation for 30 Degrees

Let's apply this to the given angle, which is 30 degrees:

1. Start with the angle in degrees: $30^\circ$
2. Multiply by the conversion factor: $30^\circ \times \frac{\pi}{180} \text{ radians}$
3. Simplify the expression: $\frac{30 \times \pi}{180} \text{ radians}$
4. Reduce the fraction. Both 30 and 180 are divisible by 30:
   • $30 \div 30 = 1$
   • $180 \div 30 = 6$
   So, the expression becomes: $\frac{1 \times \pi}{6} \text{ radians}$
5. The result is: $\frac{\pi}{6} \text{ radians}$

Therefore, 30 degrees is equal to $\frac{\pi}{6}$ radians. This matches option 2.