How many degrees are ( \frac{\pi}{4} ) radians?

Correct answer: (45^\circ)

The answer is option D, 45 degrees. Radians and degrees measure the same angle in different units. The basic conversion fact is pi radians=180 degrees. To convert pi/4 radians, divide both sides of the basic relation by 4: pi/4 radians=180/4 degrees=45 degrees. Option A, 30 degrees, would correspond to pi/6 radians, not pi/4. Option B, 60 degrees, corresponds to pi/3 radians. Option C, 90 degrees, corresponds to pi/2 radians. Option D, 45 degrees, exactly matches pi/4, so it is correct. A quick way to remember this is that a right angle is pi/2 radians or 90 degrees, and half of a right angle is pi/4 radians or 45 degrees. Do not confuse the denominator 4 with 4 degrees; the pi-to-180 conversion must be used.