What mathematical operation is used to convert radians to degrees?

To convert radians to degrees, you use the multiplication factor of ( \frac{180}{\pi} ). This conversion factor arises from the relationship between radians and degrees, where a complete circle is ( 2\pi ) radians, which is equivalent to 360 degrees. Therefore, to convert a given angle measured in radians into degrees, you multiply the measure in radians by ( \frac{180}{\pi} ).

For example, if you have an angle of 1 radian, converting it to degrees involves calculating ( 1 \times \frac{180}{\pi} ), which yields approximately 57.3 degrees. This shows that multiplying by ( \frac{180}{\pi} ) allows you to express the angle in a degree format.

Using any incorrect methods such as adding 180 degrees or dividing by 360 degrees would not yield the correct relationship between radians and degrees, resulting in a misunderstanding of how these two measurements relate to each other in terms of angles. Hence, multiplying by ( \frac{180}{\pi} ) is the precise and appropriate mathematical operation for this conversion.