How many degrees are equivalent to 1 radian?

When converting between radians and degrees, it's essential to understand the relationship between these two units of angular measurement. One complete revolution around a circle is 360 degrees, which is also equivalent to (2\pi) radians.

To find out how many degrees correspond to one radian, you can set up a proportion using the total number of degrees and radians in a circle. Since (2\pi) radians is equal to 360 degrees, you can derive the degree equivalent of 1 radian by dividing both sides of this equation:

[

1 \text{ radian} = \frac{360 \text{ degrees}}{2\pi} = \frac{180}{\pi} \text{ degrees}

]

This calculation reveals that one radian is equivalent to (180°/\pi). This ratio is a fundamental conversion factor used in various applications involving geometry and trigonometry, making it crucial for anyone studying surveying or related fields.

The other options, such as 90°, 60°, and 270°, do not accurately represent the relationship between radians and degrees, as they refer to specific angles that do not correlate to the standard conversion from radians to degrees. Specifically, 90° corresponds to