The graph of sin(sinh x) is a sinusoidal curve that has an increasing amplitude and a steeper slope as x increases. It appears similar to the graph of sin x, but with a more pronounced shape.
The key features of the graph of sin(sinh x) are its amplitude, period, and vertical shift. The amplitude is the maximum distance the curve deviates from its center, the period is the distance between each peak or trough, and the vertical shift is the amount the curve is shifted up or down from the x-axis.
To graph sin(sinh x), you can use a graphing calculator or online graphing tool. Simply input the function into the calculator or tool, and it will generate the graph for you. You can also manually graph it by plotting points using the key features of the graph (amplitude, period, and vertical shift).
The x-intercepts of the graph of sin(sinh x) occur when the function equals zero. Since sinh x is never equal to zero, the only x-intercepts occur when sin x = 0. This happens at every multiple of pi, so the x-intercepts are located at x = nπ, where n is any integer.
The domain of sin(sinh x) is all real numbers, since sinh x is defined for all real values of x. The range, however, is limited to values between -1 and 1, since sin x is bounded between those values. Therefore, the range of sin(sinh x) is [-1, 1].
