Labels:sketch | clipart | drawing | graphics | illustration | art OCR: Figure 12-13: Illustration of the Range of the Hyperbolic Sine Function It would seem that the graph of sinh is merely that of sin rotated 90 degrees. If that were so, then we would have sinh z = $sin z. Careful inspection of the shading, however, reveals that this is not quite the case; in both graphe the lightest and darkest shades, which initially are adjacent to the positive real axia, remain adjacent to the positive real axis in both cases. To derive the graph of sinh from Bin we must therefore firat rotate the complex plane by -90 degrees, then apply sin, then rotate the result by 90 degrees. In other words, sinh z = $ ain(-$)z; consistently replacing z with sz in this formula yields the familiar identity sinh iz = sain z.
