SOLUTION: convert to radian measure: 1. 85� 2.45�15'15"

Question 1010350: convert to radian measure:
1. 85�
2.45�15'15"
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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