SOLUTION: Give the greatest negative angle that is coterminal with the angle. -11π/2 -3π/2 is in the answer key, but I can’t solve it.

Algebra ->  Trigonometry-basics -> SOLUTION: Give the greatest negative angle that is coterminal with the angle. -11π/2 -3π/2 is in the answer key, but I can’t solve it.      Log On


   

Question 1204854: Give the greatest negative angle that is coterminal with the angle.
-11π/2
-3π/2 is in the answer key, but I can’t solve it.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


two angles are coterminal when the angles themselves are different, but their sides and vertices are identical
you can remember the definition of the coterminal angle as angles that differ by a whole number of complete circles

given -11pi%2F2
1 complete circle is 2pi
-11pi%2F2%2B+2pi=+-%287pi%29%2F2
-11pi%2F2%2B+4pi=+%28-3pi%29%2F2
-11pi%2F2%2B+6pi=pi%2F2....positive value, we can stop now

since we need greatest negative value, choices are -%287pi%29%2F2+ and %28-3pi%29%2F2,
since %28-3pi%29%2F2%3E-%287pi%29%2F2+, our solution is %28-3pi%29%2F2