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 ChronicCluster
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 What are Sin and Cos? 
#13250938 - 09/26/10 08:04 PM (13 years, 6 months ago) |
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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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The_Ghost
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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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 Chespirito
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blewmeanie
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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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ChronicCluster
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Re: What are Sin and Cos? [Re: blewmeanie]
#13251058 - 09/26/10 08:24 PM (13 years, 6 months ago) |
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Quote:
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.Quote:
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.Quote:
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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Ojom
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Quote:
ChronicCluster said:
WTF is the calculator doing?
It is plotting to take control of the universe!
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blewmeanie
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Quote:
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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I AM SWIM
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Re: What are Sin and Cos? [Re: blewmeanie]
#13251199 - 09/26/10 08:49 PM (13 years, 6 months ago) |
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trig functions
they are used for finding angles and thangs
http://en.wikipedia.org/wiki/Trigonometric_functions
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laserpig
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Quote:
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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Chespirito
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Re: What are Sin and Cos? [Re: laserpig]
#13251226 - 09/26/10 08:56 PM (13 years, 6 months ago) |
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Whoah man, you might want to rethink that
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laserpig
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Re: What are Sin and Cos? [Re: Chespirito]
#13251236 - 09/26/10 08:58 PM (13 years, 6 months ago) |
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you talkin' to me?
did i fuck somethin' up?
i ain't see any errors
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pwnasaurus
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Re: What are Sin and Cos? [Re: I AM SWIM]
#13251244 - 09/26/10 09:00 PM (13 years, 6 months ago) |
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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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Chespirito
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Re: What are Sin and Cos? [Re: laserpig]
#13251246 - 09/26/10 09:01 PM (13 years, 6 months ago) |
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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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laserpig
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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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islanduniverse
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Re: What are Sin and Cos? [Re: Chespirito]
#13251267 - 09/26/10 09:04 PM (13 years, 6 months ago) |
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memorize the unit circle
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laserpig
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god i hated that 
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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ChronicCluster
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Re: What are Sin and Cos? [Re: blewmeanie]
#13251281 - 09/26/10 09:08 PM (13 years, 6 months ago) |
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Quote:
Ojom said:
Quote:
ChronicCluster said:
WTF is the calculator doing?
It is plotting to take control of the universe!
 Quote:
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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luvdemshrooms
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Quote:
ChronicCluster said:What are Sin and Cos?
I like to Sin Cos it's more fun.
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ChronicCluster
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Re: What are Sin and Cos? [Re: laserpig]
#13251293 - 09/26/10 09:10 PM (13 years, 6 months ago) |
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Quote:
laserpig said:
god i hated that
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. 
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laserpig
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Quote:
ChronicCluster said:
I actually understood what you said laserpig, and it made more sense than anything else.
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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starfire_xes
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Sin and Cos are functions that map points in the X Y plane to the unit circle. They are conformal mapping functions, in that they provide for angle information to be retained in the mapping.
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Chespirito
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Re: What are Sin and Cos? [Re: laserpig]
#13251380 - 09/26/10 09:34 PM (13 years, 6 months ago) |
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Quote:
laserpig said:
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
Alright so lets say we have 3 angles, 27, 63, 90. We are trying to find out the sin(27). So now we know all the angles in the triangle. Compute the sin using your method
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laserpig
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Re: What are Sin and Cos? [Re: Chespirito]
#13251404 - 09/26/10 09:39 PM (13 years, 6 months ago) |
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you have completely misunderstood what i was trying to explain
that is not a method for computing sine or cosine, it was an explanation to help the OP understand why inputting one angle is enough info for the calculator to determine a ratio
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Chespirito
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Re: What are Sin and Cos? [Re: laserpig]
#13251421 - 09/26/10 09:42 PM (13 years, 6 months ago) |
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Oh I see, Im sorry. I thought you were saying thats how a calculator calculates the sine. And I was trying to imply that the function is nonlinear by nudging you in that direction.
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laserpig
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Re: What are Sin and Cos? [Re: Chespirito]
#13251443 - 09/26/10 09:45 PM (13 years, 6 months ago) |
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most people don't think in functions, and those that do are almost guaranteed to already have a solid grasp of what sine and cosine are
that's why i wasn't trying to explain it as a function
however you are of course correct that sine etc are nonlinear
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Inu
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Re: What are Sin and Cos? [Re: laserpig]
#13251454 - 09/26/10 09:46 PM (13 years, 6 months ago) |
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sohcahtoa!
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ChronicCluster
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Re: What are Sin and Cos? [Re: Inu]
#13251898 - 09/26/10 11:53 PM (13 years, 6 months ago) |
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Some Old Horse
Caught A Horse
Taking Oats Away.
Mine's better. It's not some random indian word.
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CaptainAhab
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what calculus are you taking?
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Fungal-one
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Once I realized that trig is a language to talk about ratios it all made sense, in a second flat, it all made sense.
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ChronicCluster
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Quote:
CaptainAhab said:
what calculus are you taking?
Calculus and analytical geometry. Of a single variable. or something.
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CaptainAhab
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ah yes. I remember that one. I've since moved on to multivariable. It's a good time. But yeah, sine is the vertical coordinate of the arc endpoint shown in this picture:
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Fungal-one
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Quote:
CaptainAhab said:
ah yes. I remember that one. I've since moved on to multivariable. It's a good time. But yeah, sine is the vertical coordinate of the arc endpoint shown in this picture:
Gif fail
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Never judge a man until you walk a mile in his shoes. But, by that time you're a mile away and you got his shoes, so fuck em.
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themostpurple
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Re: What are Sin and Cos? [Re: blewmeanie]
#13252010 - 09/27/10 12:31 AM (13 years, 6 months ago) |
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just wait until you get to non-linear equations. 
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