As per the definition of direction cosines, the cosine values of the angles formed by the directed line with the x-axis, y-axis and z-axis.

Here we consider the directed line to be the z-axis.

So from the below figure, we can say,

α = the angle formed by the z-axis with x-axis = 90°

β = the angle formed by the z-axis with y-axis = 90°

γ = the angle formed by the x-axis with y-axis = 0°

Therefore,

cos α = cos 90° = 0

cos β = cos 90° = 0

cos γ = cos 0° = 1

Hence the direction cosines of y-axis are 0, 0, 1.