Final answer:
The graph of sin(x)² oscillates between 0 and +1 and has a wavelike appearance with doubled frequency of peaks due to the squaring, which makes all sine values non-negative.
Step-by-step explanation:
The graph of sin(x)² is distinct from the basic sine function because it involves squaring the sine value at each point. Typically, the sine function oscillates between +1 and -1 with a period of 2π radians, creating a wave-like pattern. However, when you square the sine function, the negative values become positive, resulting in a graph that oscillates between 0 and +1, with a doubled frequency of peaks since both the crests and troughs in the original sine wave now become peaks in the sin(x)² graph.
The resemblance of the squared sine function graph is to a series of arches, with each arch corresponding to a single period of the sine function, and the valleys of the wave flattened out. It retains the periodic and oscillatory character typical of a simple harmonic motion, resembling a series of waves or oscillations with the amplitude being squared. The graph still has a wavelike character but without the alternating up and down motion around the axis that is seen in the basic sine function.