Integration of trig functions

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mikewill54

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Mar 7, 2016
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Hi
This is probably a basic question but any answer or recommended video is greatly appreciated. I understand why we differentiate or integrate normal functions. To give the slope of a curve or area underneath it. But what does differentiating or integrating a trig function like sin or cos tell us. I understand what sin and cos tell us about a triangle, the ratio of slope compared to the x or y axis and I also know how to integrate trig functions. I just don’t know why I’m doing it or what it tells me.
Thanks for any explanation
Thanks
 
Differentiation and integration of a trig function mean the same as for any function: The slope of the graph and the area under it. Why do you think it should be any different? I'm guessing there's some context to your question; or else you are thinking a trig function is somehow different from other functions.

Of course, in an application of trig functions, the meanings would depend on the application. For example, if the sine is being used to find the height of a seat on a Ferris wheel, then the derivative of the sine will determine how fast the chair is rising. Trig functions have many more subtle applications, and the derivative might be used for reasons having nothing to do with slopes of graphs, but it will still represent some rate of change.
 
Hi
Thanks for the reply… I’m probably thinking trig functions are different from normal functions and struggling to get my head around the integral or derivative of one.
Regards
Mike
 
mikewill54 said:
Hi Thanks for the reply… I’m probably thinking trig functions are different from normal functions and struggling to get my head around the integral or derivative of one. Regards Mike
Click to expand...
Have you done a google search for "practical application of trigonometric functions"?
 
mikewill54 said:
I’m probably thinking trig functions are different from normal functions
Click to expand...
They aren't, though they have some special properties in addition to those of other functions.

Functions are functions. And derivatives are derivatives, namely the rate of change of the function relative to its input.
 
I agree with all the helpers above. I thought I'd mention one particular use:- the cosine transform. This requires a mix of trig and integration. This is one way to obtain the frequencies present within a signal. The discrete version of this transform has been at the heart of the following for many years:- mp3 audio compression, jpeg image compression, and also mpg video compression. Online images/ audio/ video would have been delayed for a long time without this. Not everyone who starts learning this kind of calculus will use it in their future career, but some certainly do!
 
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