Hi, Can anyone give me a link to a site that explains them. First off I don't want a site with all the formulas and stuff, I know them. But a site that really explains them, what's behind them. What is a "sin", what's it stand for, how do you come up with the formula, "you know the "sin wave" how does that tie in with calculating an angle "like wtf has that got to do with it". Or if you could explain it yourself you'd be very welcome too off-course. Thanks!!! Edited by - Xyx on March 5, 2002 7:09:22 PM

try a google search for "trigonometry tutorial". trigonometry is the math of using sin, cos, tan and other fun things.

sin, cos, tan, etc are all formulas relating to right triangles (triangles containing one 90 degree angle).

as to coming up with the formula i assume by "the formula" you mean:

sin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! ...

that formula comes from using calculus to derive the Taylor Series for a function, described at the following link (obviously requires knowing some calculus to understand):
http://www.efunda.com/math/taylor_series/taylor_series.cfm

as for what the hell does a sin wave have to do with calculating an angle. well a sin wave is the graph of the function:
y = sin(x)

basically you plug in an angle X and get a number Y. plotting x and Y gives you a sin wave. by altering different parameters of the function (like changing it to sin(2x) or to 3sin(x), etc you can get different sin waves to result.

that''s the short answer, the long answer (in terms of time necessary to do) is, learn trigonometry and calculus.

-me

Thnx man!

There is an acronym that contains the essential rules of basic trigonimetry: "SOHCAHTOA." This is what it means:

sin(x) = opposite / adjacent
cos(x) = adjacent / hypotenuse
tan(x) = opposite / adjacent

Now, you're probably wondering what all these "opposites" and "adjacents" mean. Well, here's a diagram of a right triangle, with one of the angles marked with an 'x.'

             /|            / |hypotenuse /  |          /   |         /    | opposite        /     |       /x    _|      /_____|_|      adjacent  

The side across from the right angle of a right triangle is called the hypotenuse. Of the two remaining sides, one is next to the given angle, and the other is acros from it; hence the names "opposite" and "adjacent."

So here's a simple example: Bob is standing 20 ft. away from a tree. He is looking at a 30 degree angle at the top of the tree. How tall is the tree?

Well, I'll draw a diagram:

     T     'B' represents Bob.    /|     'T' represents the top of the tree   / |     'G' represents the base of the tree  /  | /x  |     We know angle TBG, which I will call 'x.'B____|G  20  

We know that angle x is 30 degrees. We also know that the length of BG is 20 ft. We want to find TG, which is OPPOSITE to angle x. Well, we look up into our trig. function definitions, and find that tan(x) = opposite / adjacent. Knowing this, we can set up the following equation:

            TGtan(30) =  ----            20  

We multiply each side by 20 to get the following result:

TG = 20tan(30)


Using a calculator, we find that TG is approximately 11.547; the tree is about 11.547 ft. tall.

So those are the basics.

Now I'll try to explain your question about sine waves.

I got rid of the triangle explanation I had posted here because (A) I made a stupid mistake and (B) It was probably just confusing. I've replaced it with a better explanation.

We know sin(x) = opposite/hypotenuse. Well, if the hypotenuse is a constant at 1, then sin(x) = opposite. Now, imagine a circle with a radius of 1. You want to find, for a given angle in that circle, what the correseponding y coordinate is, then you need only find sin(angle), because that will equal the y coordinate. Look at the following diagram:

        |  Y             This is a unit circle (r=1) centered      . |  .             at the origin.   .    | /|  .  .     |/ |   .         You can tell quickly that OY = r.--.-----|------.----     It is the hypotenuse.  Since r = 1,  .     |O X   .         sin(YOX) = XY.  This is the y coordinate   .    |     .          of the point on ths circle.      . |  .        |                cos(YOX) will give you the x coordinate. 

As you the angle increases, the point travels around the circle. Because it keeps going around it, you get the infinitely repeating wave pattern. This is also why these functions are called circular functions.

|            .|      .           .|   .                 .| .                     .                          |.-----------------------.---------------------------.-| 0          90       180 .          270           .  360|                           .                    .|                               .            .|                                      .  

This is the sine wave with the angle measures marked.

On a side note, the trigonometric functions (sin, cos, tan) included in the standard math library for C++ take angle measures not in degrees, but in radians. There are 2pi radians in a circle. You can multiply a degree measure by pi/180 to get the value in radians.

And that's it! Hopefully, this has helped explain how the familiar wave shape is related to triangles and circles. It's also found in a great many other places in nature (like in a spring bobbing up and down). But that's a topic for another post!



Edited by - TerranFury on March 9, 2002 11:46:47 AM

sin(x) = opposite/hypotenuese, not opposite/adjacent.

Code Sourcerer

Xyx,
You can goto http://www.math.com for anything related about math. Including trig functions.


Edited by - ph4ntasyph34r on March 8, 2002 10:20:30 PM

A Sin and Cos Wave are just a rolling circle, if you put a Marker on a rolling wheel it will make a sin wave

quote:

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Original post by ExplosiveNewt
A Sin and Cos Wave are just a rolling circle, if you put a Marker on a rolling wheel it will make a sin wave

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Thank you!

Sine and cosine do not define relationships for right triangles. Sine and cosine are circular functions and define a number of relations for different triangles constructed from a chord of the circle and the segment that exactly spans that chord. The sine and cosine rules, for example, are not typically used with right triangles, even though they still hold.

Sine Rule
a(sin A)^-1 = b(sin B)^-1 = c(sin C)^-1
where a, b and c are the lengths of the sides of any triangle and A, B and C are the angles opposite them respectively.

Cosine Rule
c² = a² + b² - 2ab(cos C)
with the same side and angle definitions as above.

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Thanks to Kylotan for the idea!

Yeah but when you first start trig at least in england it''s all right angled triangles.

quote:

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Original post by Crazy_Vasey
Yeah but when you first start trig at least in england it''s all right angled triangles.

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Yeah - when your 13. You get told the truth eventually...lol



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