If an angle measures \( 2 \) radians, what is its measure in degrees?

To convert radians to degrees, you can use the conversion factor \( \frac{180}{\pi} \). For an angle measuring \( 2 \) radians, you simply multiply: \[ 2 \times \frac{180}{\pi} \approx 2 \times 57.2958 \approx 114.5916 \text{ degrees} \] So, \( 2 \) radians is approximately \( 114.59 \) degrees! For a little historical twist, the radian revolutionized the way angles were viewed back in the 18th century. Mathematicians decided to use the radius of a circle as a measure for angles, which made calculations much more intuitive and easier, especially in calculus! This led to the nerdy but crucial connection between angles and arc lengths, paving the way for trigonometry as we know it today. In practical scenarios, knowing how to convert between radians and degrees is especially helpful in fields like engineering and physics. For instance, when working with oscillating systems, wave mechanics, or even in computer graphics, you'll often find these angle conversions essential for accurate calculations in simulations and designs. Being comfortable with these conversions can add a little extra flair to your problem-solving toolkit!