### Video Transcript

Convert 0.5 radians to degrees, giving the answer to the nearest second.

In this question, we need to convert an angle measure in radians to one in degrees. The most efficient way to do this is to remember that to change any angle in radian measure to one in degrees, we multiply the given angle by 180 over 𝜋. Therefore, to find the measure in degrees of 0.5 radians, we take 0.5 and multiply it by 180 over 𝜋. And since 0.5 multiplied by 180 is 90, we have 90 degrees over 𝜋. We can then use our calculator to evaluate this, making sure that the calculator is in degrees mode. This will give us 28.6478 and so on degrees.

Sometimes we might be asked to give our answer to one or two decimal places, but here we’re asked for the answer to the nearest second. And so we need to take this angle measure in degrees and convert it into one in degrees, minutes, and seconds. To do this, we take the whole number part of the answer as the answer in degrees. So we have 28 degrees. For the minutes, we multiply the remaining decimal by 60, which gives 38.873 and so on. The whole part of this answer gives us the value in minutes. So that’s 38. For the seconds, we multiply this new remaining decimal by 60. And then because we need to give the answer to the nearest second, we take this answer of 52.40 and so on and round it to the nearest whole number, which is 52 seconds.

We can then give the answer that 0.5 radians is equivalent to 28 degrees, 38 minutes, and 52 seconds to the nearest second.