Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which angle is represented by π/3 in degrees?

1. 30 degrees

2. 45 degrees

3. 60 degrees

4. 90 degrees

The correct answer is: 60 degrees

To convert the angle from radians to degrees, you can use the conversion factor that \(180^\circ\) is equivalent to \(\pi\) radians. Therefore, to convert \(\frac{\pi}{3}\) radians into degrees, you can use the formula: \[ \text{Degrees} = \text{Radians} \times \left(\frac{180^\circ}{\pi}\right) \] Substituting in the value: \[ \text{Degrees} = \frac{\pi}{3} \times \left(\frac{180^\circ}{\pi}\right) \] The \(\pi\) values cancel out, leading to: \[ \text{Degrees} = \frac{180^\circ}{3} = 60^\circ \] This demonstrates that \(\frac{\pi}{3}\) radians is indeed equivalent to \(60^\circ\). Understanding how to convert between radians and degrees is essential in trigonometry and helps in comprehending various mathematical concepts related to angles.