Need help on unit vector problem?

Question

I appreciate any help solving this problem!

Find a component form of the unit vector that makes an angle theta=

-pi/6 with the positive x-axis.

Answer 1

If vector A of magnitude |A| makes an angle θ with x-axis, its components on x-axis and y-axis are |A|cosθ and |A|sinθ.

A = (|A|cosθ) i + (|A|sinθ) j

(i and j are unit vectors on x- and y-axis)

An unit vector is nothing other than a vector with magnitude |A| = 1

u = (1.cosθ) i + (1.sinθ) j

u = cos(-π/6) i + sin(-π/6) j

u = [√(3)/2] i -  [1/2] j

Answer 2

well since it is a unit vector its magnitude = 1

I will call the two components of the vector i and j where i as horizontal and j is vertical.

sin(theta) = o/h (where h is the magnitude and o is j)

sin(-pi/6) = j/1

j = sin(-pi/6) = -0.5

cos(theta) = a/h (where a=i)

cos(-pi/6) = i/1

i = √3/2

you will need to construct a triangl,e ona diagram to fully understand what I've done but I'm your used to doing that before in your work with vectors.