Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which angle is represented by π/3 in degrees?

30 degrees
45 degrees
60 degrees
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.