Consider the function f(x, y) = -3x^2-2y^-2. Find the directional derivative of f at the point (1,-4) in the direction given by the angle theta = 2pi/5.
Find the unit vector which describes the direction in which f is increasing most rapidly at (1,-4).

I have already confirmed the directional derivative to be exactly
-6cos(2pi/5) + 16sin(2pi/5)

I believed the unit vector should have been (cos(2pi/5), sin(2pi/5)), but when I checked my answer the only correct part was the sin(2pi/5). If the other part is not cos(2pi/5), then what is it and How would that be calculated or inferred?

A picture of the original format and my answers is also included.