Question

which expression converts \\( \frac{\pi}{4} \\) radians to degrees?
\\( \frac{\pi}{4} \cdot 180^{\circ} \\)
\\( \frac{\pi}{4} \cdot \frac{180^{\circ}}{\pi} \\)
\\( \frac{\pi}{4} \cdot \frac{\pi}{180^{\circ}} \\)
\\( \frac{\pi}{4} \cdot \pi \\)

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, we use the conversion factor: \( 1 \text{ radian} = \frac{180^\circ}{\pi} \). So, to convert an angle \( \theta \) in radians to degrees, we multiply \( \theta \) by \( \frac{180^\circ}{\pi} \).

Step2: Apply the formula to \( \frac{\pi}{4} \) radians

For \( \theta = \frac{\pi}{4} \) radians, the conversion to degrees is \( \frac{\pi}{4} \times \frac{180^\circ}{\pi} \). The \( \pi \) in the numerator and denominator will cancel out, leaving us with the correct expression for the conversion.

Answer:

\( \boldsymbol{\frac{\pi}{4} \cdot \frac{180^\circ}{\pi}} \) (the second option)