Question

If \(n\) is a constant equal to the number of degrees in an angle measuring \(3 \pi\) radians, what is the value of \(n\) ?

Short answer

The value of \(n\) representing the angle in degrees is \(n = 540^\circ\).

Step-by-step solution

Understand radians and degrees

Radians and degrees are units used to express the measure of an angle. Generally, the relationship between radians and degrees is: \[1 \, \text{radian} \approx 57.2958 \, \text{degrees}\]

Define the conversion factor

To convert radians to degrees, we can use the following conversion factor: \[\frac{180^\circ}{\pi\, \text{radians}}\]

Perform the conversion

Now we are given the angle in radians, which is 3π rad, and asked to find the value of 'n' representing the angle in degrees. Apply the conversion factor: \[n = 3\pi\, \text{radians} * \frac{180^\circ}{\pi\, \text{radians}}\]

Simplify the equation

The radians unit and the π values cancel out: \[n = 3 * 180^\circ = 540^\circ\]

Write down the final answer

The final answer is: \[n = 540^\circ\]