Math Shorts - Exponential and Trigonometric Functions by Metin Bektas

Author:Metin Bektas [Bektas, Metin]
Language: eng
Format: azw3
Published: 2015-05-16T00:00:00+00:00

Let's continue with c, as this is pretty straight-forward. The constant c allows us to move the equilibrium line up (c > 0) or down (c < 0). For example, if we want to have a sine function that 1) has an amplitude of 3 units and 2) oscillates around the line y = 1, we can set a = 3 and c = 1 to accomplish that.

The graph looks like this:

Graph of f(x) = 3sin(x) + 1

Note that the maximum function value is at y = 4 (equilibrium position y = 1 plus amplitude a = 3) and the minimum value at y = -2 (equilibrium position y = 1 minus amplitude a = 3). This is true in general. Given the position of the equilibrium line at y = c, the maximum value of the function will be at y = c + a and its minimum value at y = c – a. Note that the period still remains unchanged at p = 2π. To manipulate the period p in a meaningful manner, we need to get familiar with the constant b. The key equation to keep in mind is:

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