#### Question

# 11th grade functions questions (radians)?

1a. Through how many radians does the Earth turn on its axis in a leap year? Express your answer in exact form.

b. How many hours does it take the Earth to rotate through an angle of 150 degrees?

c. How many hours does it take the Earth to rotate through an angle of 7/3 pi rad?

If someone could help me out here that would be amazing. Thanks so much! :)

#### Answers

1a) 1 revolution is 360° = 2pi radians

366 x 2pi = 732pi radians

b) 24 x 150/360 = 24 x 5/12 = 10 hours

c) 7/3 pi radians is 7/3 pi x 180/pi = 7/3 x 180 = 420°

so, 420/360 x 24 = 7/6 x 24 = 28 hours

Is that amazing? :)>

if we assume that one rotation = 1 24-hr day = 2pi radians , then

a) a leap year is 366 days, so we have 366 rotations = 366(2pi) radians = 732pi radians

b) 150/360 = 5/12 of a rotation = (5/12)(24 hrs) = 10 hrs

c)( 7 pi/3)/(2 pi) = 7/6 rotations = (7/6)(24 hrs) = 28 hrs

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