Help with tangent line to a trig function

The problem is: find the equation of a tangent line to the function y = cos2x

at the point (pi/6, .5)

i took the derivative and got -2sin2x plugged pi/6 in and got the slope to be

-(3)^.5

so i have the line y= x * -(3)^.5 + b and i plug in pi/6 for x and .5 for y and get

.5 = -(3)^.5 * pi/6 + b

so b = .5 + (3)^.5 * pi/6

i put the line equation and the original trig equation in my calculator and the line is not tangent to cos2x at that point

can someone please show me what i'm doing wrong, thank you