Question

Which expression is equivalent to cos 2 pi for all values of pi?
A) cos2pi + sin2pi
B) cos2pi – 1
C) 1 – 2 sin2 pi
D) 2 sinpi cospi

Answer 1

In radians, pi = 180 degree, Hence for 2pi = 360 degree.

For cos 0 = cos 2pi = 1

And

Sin 0 = sin 2pi = 0

While cospi = -1 and sinpi = 0

So

A)   cos2pi + sin2pi = 1 + 0 = 1

B)   cos2pi – 1 = 1 – 1 = 0

C)   1 – 2sin2pi = 1 – 2(0) = 1

D)   2 sinpi cospi = 2 * 0 * (-1) = 0

Hence “A” and “C” are correct.