Angle Conversion: Degrees to Radians
To convert an angle from degrees to radians, we use the conversion factor $\frac{\pi}{180^\circ}$.
The given angle is $54^\circ$. Applying the conversion formula:
$ 54^\circ \times \frac{\pi}{180^\circ} $
Simplifying the Expression
We need to simplify the fraction $\frac{54}{180}$. Both 54 and 180 are divisible by their greatest common divisor, which is 18.
- Divide the numerator by 18: $54 \div 18 = 3$
- Divide the denominator by 18: $180 \div 18 = 10$
Therefore, the expression simplifies to:
$ \frac{3\pi}{10} $
Final Answer
The angle $54^\circ$ is equivalent to $\frac{3\pi}{10}$ radians. This corresponds to Option 3.
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