Angles that are integer multiples of 2π often lie exactly on one of the coordinate axes.
(i) Prove that if an angle θ satisfies θ=n2π for some integer n, then its terminal side lies on one of the coordinate axes.
(ii) State precisely which axis (positive or negative branch) corresponds to each residue class of n modulo 4.
(iii) Classify the following angles according to the axis on which their terminal sides lie: 29π,−3π,−25π,14π.
(iv) Comment on whether any of the angles in part (iii) can be described as lying in a quadrant. Justify your answer.