now let's recall that a full circle has 360°, so then 1140 = 360 + 360 + 360 + 60.
namely, 1140 is 3 full-go-around the circle and then it lands on the I Quadrant at 60°. Thus cos(1140°) = cos(60°).
what's that cosine of 60°? Check the picture below.
A.
To find greater than or smaller than relation, we multiply the terms like (numerator of L.H.S with denominator of R.H.S and put the value on the left side. Then multiply the denominator of L.H.S with numerator of R.H.S and put the value on right side. Now compare the digits.)
So, solving A, we get 810<209 ... This is false
B.
= 238>589 ..... This is false
C.
= 496>780 .... This is false
D.
= 420<660 ..... This is true
Hence, option D is true.