Most experiments are formulated for the sine function. For the cosine function perform them correspondingly.
E1: Contract the quadratic array to a point, and shift it along the real axis. You will see the periodic mapping to -1 ≤ x≤ +1 . The difference of speed of movement of the points corresponds to xu = sin xz.
E2: Initialize! The array has size 1 and starts at the origin. Shift it with the x slider, or automatically with play, and observe the periodic mapping. Try to guess the curves that the lines of the array map to.
E3: Initialize again and move the array parallel to the imaginary axis with the y slider. Now you can recognize the curves at a greater distance from the origin.
E4: Initialize and choose y = - 0.5. Shift the array with the x slider or with play. Now rotation around the origin in ellipses is clearly visible.
E5: Contract the quadratic array to a point. Study the mapping of the circular array. To shift it, pull at its center. Use different radii and interpret the observations in terms of Riemann sheets.
E6: Try to calculate analytically the mapping of the quadratic array onto ellipses and hyperbolae.