Express the following angles in radians:

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. You convert degrees into radians by multiplying by a conversion factor which could be 2π radians for every 360 degrees; you could have also done π radians per 180 degrees— whichever way you like to think about it— either way you will get the same answer. So 45 times 2 over 360 reduces to 1 over 4 times this π and you get π over 4 radians that's the exact answer for the number of radians for 45.0 degrees. Then as a decimal you take π, divide it by 4 and you get 0.785 radians. 60 times 2 over 360 reduces to one-third and that means you have π over 3 radians here in 60 degrees or 1.05 radians. 90 reduces to π over 2 radians. 360 cancels with 360 on the bottom here leaving us with 2π on the top and you have 6.28 radians as a decimal. And 445 times 2 over 360 reduces to 89 over 36 times π radians and carrying out that arithmetic there, you get 7.77 radians.