Which of the following is NOT a radian equivalent of an angle measurement?

Which of the following is NOT a radian equivalent of an angle measurement?

• A. 360 degrees
• B. 2π rad
• C. π/2 rad
• D. π/3 rad

Answer: (A)

The choice of 360 degrees as the correct answer is supported by understanding the relationship between degrees and radians in measuring angles. The radian equivalent of an angle is calculated based on the relationship that \( 180 \) degrees is equivalent to \( \pi \) radians. To convert degrees to radians, the formula used is: \[ \text{radians} = \left( \frac{\text{degrees} \times \pi}{180} \right) \] Applying this formula to 360 degrees yields: \[ 360 \text{ degrees} = \left( \frac{360 \times \pi}{180} \right) = 2\pi \text{ radians} \] Therefore, 360 degrees is equal to 2π radians, making it a radian equivalent. On the other hand, 2π rad, π/2 rad, and π/3 rad are all valid radian measurements that correspond to specific angles: - 2π radians corresponds to a full circle (360 degrees). - π/2 radians corresponds to a 90-degree angle, a quarter turn. - π/3 radians corresponds to a 60-degree angle, which is one-sixth of a circle. Since

The choice of 360 degrees as the correct answer is supported by understanding the relationship between degrees and radians in measuring angles. The radian equivalent of an angle is calculated based on the relationship that ( 180 ) degrees is equivalent to ( \pi ) radians.

To convert degrees to radians, the formula used is:

[ \text{radians} = \left( \frac{\text{degrees} \times \pi}{180} \right) ]

Applying this formula to 360 degrees yields:

[ 360 \text{ degrees} = \left( \frac{360 \times \pi}{180} \right) = 2\pi \text{ radians} ]

Therefore, 360 degrees is equal to 2π radians, making it a radian equivalent.

On the other hand, 2π rad, π/2 rad, and π/3 rad are all valid radian measurements that correspond to specific angles:

• 2π radians corresponds to a full circle (360 degrees).

• π/2 radians corresponds to a 90-degree angle, a quarter turn.

• π/3 radians corresponds to a 60-degree angle, which is one-sixth of a circle.

Since