What is the equivalent of \(60^\circ\) in radians?

What is the equivalent of \(60^\circ\) in radians?

• A. \(\frac{\pi}{4}\)
• B. \(\frac{\pi}{3}\)
• C. \(\frac{\pi}{6}\)
• D. \(\frac{\pi}{2}\)

Answer: (B)

To convert degrees to radians, you can use the conversion factor that \(\pi\) radians is equal to \(180^\circ\). To find the equivalent of \(60^\circ\) in radians, you set up the conversion as follows: \[ \text{radians} = 60^\circ \times \frac{\pi \text{ radians}}{180^\circ} \] When you simplify this, you get: \[ \text{radians} = 60 \times \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3} \] Thus, \(60^\circ\) is equivalent to \(\frac{\pi}{3}\) radians. This is important in trigonometry and other areas of mathematics, where radians are often a preferred unit of measure because they relate the angle directly to the arc length for a circle. The correct answer, therefore, is \(\frac{\pi}{3}\).

To convert degrees to radians, you can use the conversion factor that (\pi) radians is equal to (180^\circ). To find the equivalent of (60^\circ) in radians, you set up the conversion as follows:

[

\text{radians} = 60^\circ \times \frac{\pi \text{ radians}}{180^\circ}

]

When you simplify this, you get:

[

\text{radians} = 60 \times \frac{\pi}{180} = \frac{60\pi}{180} = \frac{\pi}{3}

]

Thus, (60^\circ) is equivalent to (\frac{\pi}{3}) radians. This is important in trigonometry and other areas of mathematics, where radians are often a preferred unit of measure because they relate the angle directly to the arc length for a circle.

The correct answer, therefore, is (\frac{\pi}{3}).