Trig Functions Without Amplitude

harpazo

harpazo

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I know that sine and cosine have an amplitude. However, the remaining trig functions do not. Why is that the case??
 
Other trig functions, like [MATH]A\tan(Bx+C)+D[/MATH], have a scale factor ([MATH]A[/MATH]) that is not an amplitude because it does not represent a maximum deviation from the base value ([MATH]D[/MATH]); I sometimes describe it as a "pseudo-amplitude", because it can be used in a similar way in graphing.
 
Dr.Peterson said:
Other trig functions, like [MATH]A\tan(Bx+C)+D[/MATH], have a scale factor ([MATH]A[/MATH]) that is not an amplitude because it does not represent a maximum deviation from the base value ([MATH]D[/MATH]); I sometimes describe it as a "pseudo-amplitude", because it can be used in a similar way in graphing.
Click to expand...

What do you mean by a MAXIMUM DEVIATION FROM THE BASE D?
 
Can you not see what my words mean, and make an attempt at understanding how they fit into this context? I assumed you could, and intentionally challenged you to think, because that's important in learning math.

Deviation means moving away from something. You know that D is the value of y that forms the middle of the graph (the x-axis when D=0), so that's what I mean by "base". So I'm saying that the amplitude is the largest (maximum) distance (deviation) above or below the horizontal line through the middle of the graph.

Again, the graph of sine or cosine rises to a peak and falls to a valley, if you like those terms. The amplitude is how far it goes above and below the middle line on the graph, which I here called the "base" (I've seen a variety of terms used for it, such as "midline").

The tangent and secant have no maximum, so there is no technical "amplitude" (no farthest up or farthest down).
 
Dr.Peterson said:
Can you not see what my words mean, and make an attempt at understanding how they fit into this context? I assumed you could, and intentionally challenged you to think, because that's important in learning math.

Deviation means moving away from something. You know that D is the value of y that forms the middle of the graph (the x-axis when D=0), so that's what I mean by "base". So I'm saying that the amplitude is the largest (maximum) distance (deviation) above or below the horizontal line through the middle of the graph.

Again, the graph of sine or cosine rises to a peak and falls to a valley, if you like those terms. The amplitude is how far it goes above and below the middle line on the graph, which I here called the "base" (I've seen a variety of terms used for it, such as "midline").

The tangent and secant have no maximum, so there is no technical "amplitude" (no farthest up or farthest down).
Click to expand...

Yes, I prefer the MATH FOR DUMMIES style of language. I am not just interested in finding the answer. I want to understand what I'm doing, the process to get the answer.
 
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