Convert ( \frac{23\pi}{12} ) radians into degrees.

Correct answer: (345^\circ)

The answer is option C, 345 degrees. Use pi radians=180 degrees. In 23pi/12, each pi corresponds to 180 degrees, so the value is (23/12) times 180 degrees. Since 180/12=15, this becomes 23 times 15=345 degrees. Option C is therefore correct. Option A, 335 degrees, is 10 degrees too small and would correspond to a different radian value. Option B, 340 degrees, is also not the result of multiplying 23 by 15. Option D, 355 degrees, is 10 degrees too large. A useful check is that 23pi/12 is one pi/12 less than 2pi, because 2pi=24pi/12. One pi/12 equals 15 degrees, so 360-15=345 degrees. Be careful not to round a value close to 360 degrees to 360; exact conversion is required.