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If you have a trig function $f(x) =- 3\sin (2x) + 1$ then would you ever say that the amplitude is negative? I've seen it stated that it can be negative or that amplitude is a distance so it should only be a positive value. I'm wondering if it depends on the context of the problem. But if I'm talking about a general function with no context, would I always say that the amplitude is positive and then the function is "flipped"?

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  • $\begingroup$ I've seen and heard the term abused as a sort of "short-hand" for saying that the bounded trig function has been "vertically inverted" (multiplied by -1). The proper definition is to take half the difference of the maximum value minus the minimum value, which will produce a positive value (as also discussed in answers below). $\endgroup$ – colormegone May 21 '14 at 20:27
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The amplitude, because otherwise the amplitude would depend on the phase: if you shift the $\sin$ function by $\pi$, it becomes $-\sin$. You don't really want to have what you call the amplitude depend on something as arbitrary as where the function crosses zero. Another example: what would the amplitude of $\sin(x-\pi/4) = -\sin(x+3\pi/4)$ be?

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  • $\begingroup$ That's a really good point and example. So if I were describing the graph −sin(x+3π/4) in its parts, could I state that there is a phase shift of 3π/4 to the left and it's vertically inverted? $\endgroup$ – tazboy May 21 '14 at 21:04
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    $\begingroup$ @tazboy You could certainly state that, but whether that is useful/meaningful depends on the context. Remember that we could just as well have written it as $-\cos(x+\pi/4)$. I can't think of many cases where it is useful to make a distinction between these identical functions. $\endgroup$ – user111187 May 22 '14 at 4:35
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Amplitude is positive as far as I know. its one half the positive difference of the maximum and minimum values. Think of it this way, it is the distance of the maximum and minimum from the Centre axis. For example we have a function $y=-sin(3x)$ the amplitude of this function is amplitude=|a|=|-1|=1. Let me know if you need further help or suggestions.

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