Convert 142 degrees, 46 minutes, and 48 seconds to radians, giving the answer to three decimal places.
In this question, we need to convert this angle given in degrees, minutes, and seconds to an angle in radian measure. In order to perform a conversion, we can remember that to convert an angle in degrees to an angle in radians, we multiply the given angle by 𝜋 over 180.
But because we are given the angle in degrees, minutes, and seconds, the first thing we need to do is to convert this angle into one which is in degrees only. So 142 degrees, 46 minutes, and 48 seconds will have a whole number of degrees as 142. We can then add on 46 minutes over 60 minutes and then 48 seconds over 3600 seconds. Using a calculator, we can work this out as 142.78 degrees.
Now we are ready to convert this angle in degrees into one in radians. And therefore, we have 142.78 multiplied by 𝜋 over 180 radians. Using our calculators once again, we can evaluate this as 2.49198 and so on radians. As we need to give the answer to three decimal places, we check the fourth decimal digit to see if it is five or more. As it is, then we round the answer up to 2.492 radians.