cos(3.5x+5.5)=0.1263, 3.5x+5.5=cos-1(0.1263)=1.444158 radians approx.
Since, for all angles A, cos(A)=cos(-A)=cos(2π-A), cos-1(0.1263)=2π-1.444158=4.839027.
Therefore, 3.5x+5.5=1.444158+2πn or 4.839027+2πn where n is an integer.
3.5x=1.444158+2πn-5.5 or 4.839027+2πn-5.5. The smallest positive value of n which allows x to be positive is 1. Therefore, 3.5x=-4.055842+2π=2.227343 or -0.660973+2π=5.622212.
x=2.227343/3.5=0.6364 or 5.622212/3.5=1.6063 approx.
x=0.6364, 1.6063.