Which angles are coterminal with 5p/4?

Question

Which angles are coterminal with 5π/4?

A.π/4

B.9π/4

C.13π/4

D.-3π/4

Answer 1

For any angle, if you add or subtract 2π you go around the entire circle and come back to the same point.  So to find if an angle is coterminal with another angle, find the different between them.  If the difference is a multiple of 2π, then the angles are coterminal.

 

So what is the difference between 5π/4 and each of the choices:

 

A:  5π/4 - π/4 = 4π/4 = π    --  NO

B:  5π/4 - 9π/4 = -4π/4 = -π   -- NO

C:  5π/4 - 13π/4 = -8π/4 = -2π   --  YES

D:  5π/4 - (-3π/4) = 8π/4 = 2π -- YES

 

So the answer is C and D