(i) Show that the graph of y=cosx can be obtained from the graph of y=sinx by a translation. State clearly the magnitude and direction of this translation.
(ii) Verify your result in part (i) by listing four corresponding key points on the two graphs and demonstrating how each point on one graph maps to the other after the stated translation.
(iii) On a single set of axes, first sketch y=sinx for x∈[0,2π]. Then, without plotting a fresh set of points, obtain the graph of y=cosx using the translation identified in part (i). Label all intercepts, maxima and minima for both graphs.
(iv) Using the combined sketch, explain why the graphs of y=sinx and y=cosx never intersect at their respective maximum or minimum points.