A student wishes to compare the graphs of two trigonometric functions over x∈[−π,π].
(a) Prepare an ordered pair table for y=cosx at x=−π,−2π,0,2π,π.
(b) Using the same set of x-values, prepare an ordered pair table for y=sin(2π−x).
(c) Plot both sets of points on the same set of axes and sketch smooth curves through them.
(d) From your sketch, state the relationship between the two graphs and explain why this is consistent with a standard trigonometric identity.
(e) Comment on any phase shift observed between the two periodic curves.