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What are Sin and Cos?
    #13250938 -

So, basically here is a pretty "simple" question.

Right now in Calculus we are talking about the trig functions.
No Math teacher that I have ever had has actually tried to teach what those actually are.  What they mean.  I'm slightly depressed by the fact that people hundreds of years ago knew what these were, and no one seems to know in the present day.
Or at least, we are not taught what they are, only how to use them.

I know the simple things, such as sin and cos can be used to find the angle or the length of a line in a right triangle.
But now we are getting into stuff like the derivative of sin(x) is cos(x) and cos(x) is -sin(x)

Now can someone explain to me what the terms "sin" and "cos" actually mean?  and please do not say something like sin = 1/csc or whatever.  the words sin or cos should not be in the definition.


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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13250949 -

Thats what always screwed me over in the way math is taught. They just tell you do shit without explaining it.


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/ / / / / / / LISTEN TO MY MUSIC: E X E D / / / / / / /
The universe gives no fucks. And takes no fucks.
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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13250951 -

http://en.wikipedia.org/wiki/Sine

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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13250961 -

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse, and the cosine is the ratio of the length of the adjacent side to the length of the hypotenuse.


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Re: What are Sin and Cos? [Re: blewmeanie]
    #13251058 -

Chespirito said:
http://en.wikipedia.org/wiki/Sine


I am not a math major, that does not make sense to me. That was the first place I looked before posting. Thanks for trying though.
The_Ghost said:
Thats what always screwed me over in the way math is taught. They just tell you do shit without explaining it.


Yup, I call it "pushing numbers around"  usually no one has any sort of idea what the numbers actually mean, or where they come from.
blewmeanie said:
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse, and the cosine is the ratio of the length of the adjacent side to the length of the hypotenuse.


I mean I know that.  You can use them to get the length or the angle.  I still don't understand why that is important though.  I also don't understand how you can plug sin(some number) into your calculator, and have it spit out a decimal number.
WTF is the calculator doing?


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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13251112 -

ChronicCluster said:
WTF is the calculator doing?


It is plotting to take control of the universe!

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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13251166 -

ChronicCluster said:
I mean I know that.  You can use them to get the length or the angle.  I still don't understand why that is important though.  I also don't understand how you can plug sin(some number) into your calculator, and have it spit out a decimal number.
WTF is the calculator doing?


Opposite/hypotenuse = sine


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Re: What are Sin and Cos? [Re: blewmeanie]
    #13251199 -

trig functions

they are used for finding angles and thangs

http://en.wikipedia.org/wiki/Trigonometric_functions


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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13251219 -

ChronicCluster said:
I mean I know that.  You can use them to get the length or the angle.  I still don't understand why that is important though.  I also don't understand how you can plug sin(some number) into your calculator, and have it spit out a decimal number.
WTF is the calculator doing?


when you plug sine or cosine into your calculator, you give it an angle
since sine and cosine only apply to right triangles, one angle is enough to give a complete description of the triangle's shape
(say you input 32 degrees ... well, the calculator knows a right triangle has a 90 degree angle, and it knows the sum of all angles is 180, so 180 - 90 - 32 = 58 ... voila, a complete description of the triangle's shape)
based on knowing the triangles shape, the calculator then outputs a number
that number is the ratio between sides of the triangle (ie, the length of one side divided by the length of another)
which side is compared to which other side depends on the function (ie, sine is one ratio, cosine is a different ratio, etc), but that's the process your calculator is doing

why do you need this ratio?
depends on what you're doing -- some functions require it, and that's where you use sin/cos/etc
it depends entirely on what you're using the math for


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Re: What are Sin and Cos? [Re: laserpig]
    #13251226 -

Whoah man, you might want to rethink that

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Re: What are Sin and Cos? [Re: Chespirito]
    #13251236 -

you talkin' to me?
did i fuck somethin' up?
i ain't see any errors


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Re: What are Sin and Cos? [Re: I AM SWIM]
    #13251244 -

When you start talking about derivatives, it's not very simple to just 'explain' where it comes from.

Sine and cosine are actually modeled as complex exponential functions.

sin(x) = (e^(ix) - e^(-ix))/2i

If you differentiate that, you come out with -cos(x) - if you take a course on complex analysis this would make a lot more sense, but that is pretty complex math.  For your purposes, I would say just accept that it is the ratio of sides and not try to understand it any more than that.

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Re: What are Sin and Cos? [Re: laserpig]
    #13251246 -

I guess I dont see how what you said makes any sense.  So you're saying that to find the sin(x) you find out the other angle i.e. 180-x?  Then what do you do with this information?  Keep in mind that sine is nonlinear

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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13251260 -

i'm saying that one angle (as long as it's not the right angle) is enough to define the whole shape of a right triangle

once the calculator "knows" the shape of the triangle, it necessarily also knows (by which i mean, it can calculate) the ratios between any two sides

since sine, cosine, etcetera, are just ratios between sides, that's why you can input a single number and get a useful output

i was responding to the OP's question here:
Quote:
ChronicCluster said:
I also don't understand how you can plug sin(some number) into your calculator, and have it spit out a decimal number.
WTF is the calculator doing?



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Re: What are Sin and Cos? [Re: Chespirito]
    #13251267 -

memorize the unit circle


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Re: What are Sin and Cos? [Re: islanduniverse]
    #13251278 -

god i hated that :lol:

the unit circle is fantastically useful, but the only way it can possibly be remembered (or even understood as important) is after using those functions over and over and over again

unfortunately, in standard education, they try to teach it to you before you use all of those functions, so there's no way a student can understand why they should care or even what the f*ck those numbers are supposed to mean


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Re: What are Sin and Cos? [Re: blewmeanie]
    #13251281 -

Ojom said:
ChronicCluster said:
WTF is the calculator doing?


It is plotting to take control of the universe!


:ilold:
I AM SWIM said:
trig functions

they are used for finding angles and thangs

http://en.wikipedia.org/wiki/Trigonometric_functions


Thank you for reading the other posts before you posted.

I actually understood what you said laserpig, and it made more sense than anything else.

Also, pwnasaurus, with the horrible technique with which they try to teach math, I'm staying the fuck away from that.  They basically tell you to figure it out yourself.
I've learned more about math in math-based classes than i have in math classes.


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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13251290 -

Quote:
ChronicCluster said:What are Sin and Cos?


I like to Sin Cos it's more fun.


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Re: What are Sin and Cos? [Re: laserpig]
    #13251293 -

laserpig said:
god i hated that :lol:

the unit circle is fantastically useful, but the only way it can possibly be remembered (or even understood as important) is after using those functions over and over and over again

unfortunately, in standard education, they try to teach it to you before you use all of those functions, so there's no way a student can understand why they should care or even what the f*ck those numbers are supposed to mean


Agreed.  I have it memorized.  (they showed us a few tricks)  I still don't know why it's important.  You use it to figure out problems when the problem looks like it needs it.  :shrug:


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Re: What are Sin and Cos? [Re: ChronicCluster]
    #13251295 -

ChronicCluster said:
I actually understood what you said laserpig, and it made more sense than anything else.


:highfive:

Quote:
I've learned more about math in math-based classes than i have in math classes.


and you always will
i would have no fucking idea how to do math if i hadn't taken so much physics


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