first quadrant is from 0 to pi/2 , second is from pi/2 to pi , third quadrant is from pi to 3 pi/2, fourth quadrant is from 3 pi/2 to 2 pi as total circle is of 2 pi

complete circle is divided into four quadrants

22 pi/3 = 7 pi + pi/3

= 6 pi + 4 pi/3

4 pi/3 = 180 + 60 ; which comes under third quadrant

therefore in third quadrant we have negative values i.e. both x and y are negative

cos(22 pi/3) = - 1/2

sin(22 pi/3) = - 3^(1/2)/2 , hence both cos x and sin x have negative signs