What is the degree measure equivalent to π rad/4?

What is the degree measure equivalent to π rad/4?

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 90 degrees

Answer: (B)

To convert radians to degrees, you use the conversion factor that \(180\) degrees is equivalent to \(\pi\) radians. This means you can convert a radian measure to degrees by multiplying it by \(\frac{180}{\pi}\). In this case, we want to convert \(\frac{\pi}{4}\) radians to degrees. Using the conversion factor: \[ \frac{\pi}{4} \text{ radians} \times \frac{180 \text{ degrees}}{\pi} = \frac{180}{4} \text{ degrees} = 45 \text{ degrees} \] This calculation is correctly derived from the fundamental relationship between radians and degrees and confirms that the angle measure \(\frac{\pi}{4}\) radians is equal to \(45\) degrees. Thus, \(45\) degrees is the correct equivalent of \(\frac{\pi}{4}\) radians.

To convert radians to degrees, you use the conversion factor that (180) degrees is equivalent to (\pi) radians. This means you can convert a radian measure to degrees by multiplying it by (\frac{180}{\pi}).

In this case, we want to convert (\frac{\pi}{4}) radians to degrees. Using the conversion factor:

[

\frac{\pi}{4} \text{ radians} \times \frac{180 \text{ degrees}}{\pi} = \frac{180}{4} \text{ degrees} = 45 \text{ degrees}

]

This calculation is correctly derived from the fundamental relationship between radians and degrees and confirms that the angle measure (\frac{\pi}{4}) radians is equal to (45) degrees. Thus, (45) degrees is the correct equivalent of (\frac{\pi}{4}) radians.