NICET - Highway Construction Inspection Practice Exam

How do you convert degrees to radians?

1. Degree * π/180

2. Degree * 180/π

3. Radian * 180

4. Radian * π/180

The correct answer is: Degree * π/180

Converting degrees to radians involves using the relationship between them, which is based on the fact that a full circle is represented as 360 degrees or \(2\pi\) radians. To find the radian equivalent of degrees, you multiply the number of degrees by \(\pi\) and then divide by 180. This conversion factor comes from the equation \( 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \). Therefore, when you multiply degrees by \(\frac{\pi}{180}\), you effectively adjust the scale from degrees (which are base 10 multiples of 360) to radians (which are base multiples of \(\pi\)). For example, converting 180 degrees gives: \[ 180 \times \frac{\pi}{180} = \pi \text{ radians} \] This approach is consistent with the units involved and is essential for calculations in trigonometry, calculus, and physics where radians are preferred due to their direct relationship with arc lengths and angles in circular motion.