Question 1010350
radians = degrees * pi / 180


degrees = radians * 180 / pi


problem 1:


85 degrees * pi / 180 = 85/180 * pi = .472222... * pi radians = 1.483529864 radians.


problem 2:


45 degrees 5 minutes 15 seconds is equivalent to 45.0875 degrees.


45.0875 degrees * pi / 180 = 45.0875/180 * pi = .2504861111 * pi radians = .7869253265 radians.


how to check if we did this right?


the number of degrees in a circle is 360.


the number of radians in a circle is 360 / 180 * pi = 6.283185307.


85 degrees / 360 = .236111111
1.483529864 / 6.283185307 = .236111111


they're the same indicating the angles are the same.


45.0875 / 360 = .1252430556
.7869253265 / 6.283185307 = .1252430556


they're the same indicating the angles are the same.


key concept review:


degrees = radians * 180 / pi


radians = degrees * pi / 180


degrees = minutes / 60


degrees = seconds / 3600.


using the degree formulas:


45 degrees 5 minutes 15 seconds = 45 degrees + 5/60 degrees + 15/3600 degrees = 45.0875 degrees.


your solutions are:


1.
85 degrees = 1.483529864 radians.


2.
45 degrees 5 minutes 15 seconds = .7869253265 radians.


the measures are not exact.
they are approximate rounded to the number of decimal places shown.