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March 11th, 2009, 11:42 AM   #1
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sine, cosine, etc

Please forgive me for asking all of these very simple questions, but I am teaching myself mathematics because I was a very poor student in high school and never paid any attention in my maths classes and now I am very interested in math/science. I must know the underlying logic behind a concept to actually learn it.

So, that being said, on to my question.

How does the sine, cosine, tangent, etc, become useful? For example, what is the purpose behind taking the opposite side and dividing it by the hypotenuse? What is it for?
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March 11th, 2009, 12:07 PM   #2
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Re: sine, cosine, etc

First answer off the top of my head would be that said trig operations allow one to calculate angles based off of measurements of a triangles sides -- this is done using the inverse functions of those operations. The same logic goes the other way around. With the angle and the knowledge of one or two sides of the triangle (depending on the triangle in question) you can determine the lengths of the other sides.

Other uses are more or less based on just those two properties.
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March 11th, 2009, 05:28 PM   #3
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Re: sine, cosine, etc

Trigonometric functions become very useful in more complicated mathematics. Once you learn the unit-circle definition they become much more useful in proofs and can be more accurately defined quantity wise using special right triangles for reference. In Calculus they can be defined as a Taylor series expansion (trig functions described as an infinite polynomial) which can be used to determine extremely accurate approximations of the function. Also in Calculus their basis off of right triangles allows us to simplify difficult or otherwise impossible integration problems by using them for substitution due to their simplistic integrable/differentiable nature.
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March 12th, 2009, 08:44 AM   #4
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If you need to warn of a 1 in 6 incline, would it be more convenient to refer to that incline as a 9.46 incline? Which is easier to measure? The tangent function helps you confirm the two are approximately equivalent.
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March 12th, 2009, 09:55 AM   #5
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Re: sine, cosine, etc

I'm having some slight trouble wrapping my head around the concept. I think I know what it is, but I can't articulate it. Maybe once I study more, they'll become evident? Thanks a lot for answering though
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March 12th, 2009, 08:55 PM   #6
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Re: sine, cosine, etc

As you progress further into trigonometry you will get other definitions of the trigonometric functions, such as the unit circle I mentioned. Because, as you will learn later, there are many many trigonometric identities such as $\displaystyle \sin^2x+\cos^2x=1$ you can use them to radically simplify certain relations. Trigonometric functions really clicked with me finally when I studied sequences and series in calculus, as the Taylor series really sheds some light on the subject.

Last edited by skipjack; February 28th, 2018 at 01:18 PM.
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March 12th, 2009, 10:17 PM   #7
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Re: sine, cosine, etc

I thought that maybe perhaps I must study further to be able really understand these concepts. Maybe I need to be more patient.
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