Determine the value of cos1110°

#### Question

#### Answer

Since the cosines function has a period of 360° or 2\pi, the value of cos1110° is equal to the remainder after 1110° divided by 360, that is

1110° \mod 360 = 30°

Therefore

\cos1110° = \cos30°=\dfrac{\sqrt{3} }{2}

which is approximately equal to

\dfrac{1.73205}{2} \approx 0.866

Using Cofunction Identity

\cos30\degree = \cos(90\degree - 60\degree ) =\sin60\degree

Therefore, \cos1110°, \cos30° and \sin 60\degree have the same value.