find an angle between 0 degrees and 360 degrees that is coterminal with 900 degrees

Question

a. find an angle between 0 and 360 degrees that is coterminal with 900 degrees

b. find an angle between 0 and 2pie that is coterminal with (-12pie)/7

Answer 1

coterminal angles sum to a multiple of 360 degrees; coterminal angles start and end in the same place

a) 900º makes 2 1/2 revolutions: 360+360+180=900

    a coterminal  angle with 900º would be 180º (and -180º, but this is negative)

    another coterminal angle with 900º would be 540º (360+180) but 540 is not between 0 and 360

 b) (-12pi)/7 turns 180º and then another 5/7 of a 180º turn

     a coterminal angle would be (2pi)/7

     (-12pi)/7 is 308 4/7 degrees, 360-308 4/7=51 3/7 degrees which is (2pi)/7

     another coterminal angle would be (16pi)/7 but that exceeds 2pi

     another coterminal angle would be (-26pi)/7 but this is less than 0