(a) State the domain and range of the parent functions and . (b) Describe with…
MATHEMATICS · Subjective · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
(a) State the domain and range of the parent functions y=sinx and y=cosx.
(b) Describe with reasons whether each of the two graphs in part (a) represents an even function, an odd function or neither.
(c) Using part (b), explain how the symmetry of the graphs helps in reducing the effort required to sketch them over the interval [−2π,2π].
(d) Draw neat, labelled sketches of y=sinx and y=cosx on the same set of axes for x∈[−2π,2π]. Clearly mark all intercepts, maxima, minima and points of intersection of the two graphs.
(e) Based on your sketches in part (d), write two observations comparing the relative positions of corresponding key points on the two graphs (for example, compare the first maximum of one graph with a suitable point on the other).