Draw the graph of y = 2 sin (x/2 + pi/4) and find its properties

Question:

Function y = 2 sin (x/2 + pi/4) represents a simple harmonic motion. Find its amplitude, cycle (period), frequency, and initial phase and draw the graph.

The standard sine function is: y = A sin (Bx + C), in which A is the amplitude, B is the frequency, and C is the initial phase. The cycle (period) T = 2pi/B.

Draw the graph of y = 2 sin x/2 first, then shift the graph of y = 2 sin x/2 left pi/2 units to get the graph of y = 2 sin (x/2 + pi/4). Watch the video for the very detailed solution.