1 radian equals how many degrees, minutes, and seconds

1 radian equals how many degrees, minutes, and seconds?

The correct answer and explanation is:

1 radian is equal to approximately 57.2958 degrees. To convert this into degrees, minutes, and seconds:

1. First, note that 1 degree equals 60 minutes and 1 minute equals 60 seconds.
2. Start with 57.2958 degrees. The whole number is 57 degrees.
3. Take the fractional part, which is 0.2958, and multiply it by 60 to convert it into minutes: 0.2958×60=17.748 minutes0.2958 \times 60 = 17.748 \text{ minutes} So, you have 17 minutes and a fractional part of 0.748 minutes.
4. Multiply the fractional part 0.748 by 60 to convert it into seconds: 0.748×60=44.88 seconds0.748 \times 60 = 44.88 \text{ seconds} This rounds to 45 seconds.

Thus, 1 radian is approximately equal to 57 degrees, 17 minutes, and 45 seconds.

This conversion comes from the fact that a full circle is 360 degrees, which is equivalent to 2π2\pi radians. Since 2π2\pi radians equals 360 degrees, 1 radian equals 3602π\frac{360}{2\pi} degrees. The calculation results in approximately 57.2958 degrees per radian. Understanding the relationship between radians and degrees is important in fields like mathematics, physics, and engineering, where angular measurements are often required.