Thanks. But how did you know you can use sin? The answer used cos for both, they used the formula costheta = a1/|vector|.
What I did was just using the unit circle. x=cos(theta) and y=sin(theta), and radius/modulus/length is 1.
For a question like this, it would be easier using sin and cos, but what I'm guessing they did was a.b=|a||b|costheta so v.i=1*1*costheta, x = cos(30) = (√3)/2 where x is the component of the unit vector in the i direction, and v is the unit vector
v.(-j) = -y=1*1*cos(60º)=1/2 so y= -1/2 where y is the component of the unit vector in the j direction (because it's multiplied with the unit vector in the negative j direction, it's -j). If it were multiplied by j (unit vector in the positive direction, up) it would be y = 1*1*cos(120º)= -1/2 (same answer), it's just the angle that would change.
Sorry for the horrible notation, I'm rusty but I hope you can follow my reasoning