t is not 30°. t is arctan(1/2). And so your coordinates (cos(2t),sin(2t)) = ?
I have to find the coordinates for S(i).
My attempt :
OP = 1 * 1/2 = 1/2
(1/2)^{2} + x^{2 }= 1^{2}
x = √(3)/2
cos^{-1}(√(3)/2) = 30
sin^{-1}(1/2) = 30
t = 30
cos(2*t) = cos(60) = 1/2
sin(2*t) = sin(60) =√(3)/2
S(i) = (1,2 , √(3)/2 )