(a) Use a graphing utility to graph the function and approximate the maximum and minimum points on the graph in the interval [0, 2π), and (b) solve the trigonometric equation and verify that its solutions are the x-coordinates of the maximum and minimum points of f. (Calculus is required to find the trigonometric equation.)
1. f (x) = sin2 x + cos x
2. f (x) = cos2 x − sin x
3. f (x) = sin x + cos x