SRL Archive - OSR Advanced Scripting Tutorials

You've come here, because, apparently, you're interested in trigonometry (or at least trigonometric ratios). :)


I'm not actually in a trig class, but I have apparently "re-discovered" the lost art of what some say may be the fabled self-teaching. (Well, I just actually looked up the math and got out a piece of paper and a compass, but its not that hard, really!) And to those of you are thinking: "ZOMG!?! He's doing math at home?", at least its better that Literature. :rolleyes:


First you need to have had at least some experience with some of this, so no Jocks (AKA math newb) in this thread please. I'd like you to get out (maybe) a dictionary and open up a browser and navigate to google if you think you might need to look up the math and/or look up some of this stuff.


Now… I expect you to know these:

• Line
• Line segment
• Ray
• Angle
• Triangle

If you don't know those, please, go to http://www.dictionary.com and http://www.google.com and look 'em up.


I think I can finally start explaining. So, if you know what a line is, its a 1D/2D (can't remember which, but I think 2D is for planes and/or angles etc.) shape thingy mabob that goes on forever (grasp that concept before we continue) in both directions. You label it with two points, and you name these points according to alphabetic order starting with A. You'd then move onto AA, AB, and all that. You happen to write that something is a line by drawing a line with arrows on both sides above the two points on a line.

Now, a line segment, unlike a line, has a finite amount of space it occupies. It doesn't go on forever. You still label it with two points, with the same conventions as before. Do write its symbol, its just a line above the two letters that make it up.

A ray, somewhat like a line, does continue on for an indefinite amount of space, but only in one direction. Now, unlike Lines and Line segments, you do have to name this a special way, with the endpoint of the ray first. The symbol is a line, with a arrow pointing right, above the two letters.


Example (excuse the non-straight lines atm, no pics on google and I can't find a ruler):

So an angle is just two rays that share the same endpoint, called a vertex. Pound it into your head. You'd define an angle by writing a triangle without its right side, and then the three points of the angle. A point that both rays start at, and the two points that are on the sides of the angle. (You can also just put the vertex after the angle symbol, and you might want to google some of these pictures. I don't feel like taking up to much space). Now, there are four classifications I am aware of: Acute (less than 90deg but not 0deg), right (90deg), obtuse (greater that 90deg but not 180deg), and strait (180 deg).

So, as long as the angle is acute, we can make it a right triangle by extending the rays (I told you, they go on forever. We can cover what you do with obtuse angles later).

To move forward, we need to create an imaginary triangle… Heres a picture

Heres what this is all about. Points A, B, and C are the vertexes of the triangle. Lines a and b are the "legs", or the lines that are on the right angle. c is the hypotenuse, the length of the line opposite of the right angle.

The Pythagorean theorem goes like this:

a^2 + b^2 = c^2
So you don't need to draw a line to connect the points of a right angle.

That means c, the hypotenuse, is simple the square root of the answer to the formula… Sadly, its almost always not a whole number :p

What we can do with the hypotenuse is get the sine and cosine of the various angles. Therefore,

Sine of A = a/c
Sine of B = b/c

Cosine of A = b/c
Cosine of B = a/c

Tangent of A = a/b
Tangent of B = b/a

Nifty, eh?


What you can use these values for is really up to what you want to do… Most of it was discovered by math geniuses way-back-when.


The next three are cotangent, secant, and cosecant. They are the following:

Cotangent of A = b/a
Secant of A = c/b
Cosecant of A = c/a

You can use google to find out a whole bunch of things about the rest of this stuff, I'm just here to get you interested.



Thats pretty much it, how confusing did I make it?

haha good job.

One thing though :D

Paint has a line tool xD

Did Pythagora use the " :p " there? xD

Maybe tell about the secant, cosecant, and cotangent.

From: Pythagoras
I have made up a mathematical sentence that I have been working on for a very long time. Do not let it disturb you.

A^2+B^2=C^2 :p

The last smiley displays…

Originally, the nerd that found this sentence written down in an ancient .txt file in Greece, just thought that Pythagoras was 1337. He missed the last sentence telling what ":p" was for. We may never get to know.

Lol :p

Good tut. I didn't want to look up all the things so I skipped it :D Maybe add a section on how to use it?

-Knives

Also, robot, maybe make an example like this about hypotenuse, if some people don't understand the dictionary of the text, because I think no-one is going to dictionary.com xD

Function Hypotenuse(A, B: Extended): Extended;
Begin
  Result := Sqrt(Sqr(A) + Sqr(B));
End;

Function Hypotenuse2(A, B: Extended): Extended;
Begin
  Result := Sqrt(A * A + B * B);
End;

and about how to use them :), like u can make curvy lines!!!
:):):):):):):):):)

and how to make the stuff like this http://images.google.com/imgres?imgurl=http://www.physics.upenn.edu/courses/gladney/mathphys/images/group_d_cosine.gif&imgrefurl=http://www.physics.upenn.edu/courses/gladney/mathphys/gallery.html&h=461&w=458&sz=5&hl=en&start=10&sig2=QSuJ0JYdC1PPU5MEf-ZJLA&tbnid=ib9Hm8U7W2RReM:&tbnh=128&tbnw=127&eid=HExYR4yaApuWeIuD-MsO&prev=
on graphing calculators :P

N3ss3s, I gave them the formula to get the hypotenuse. :)

But I'm surprised this didn't get left to rot…

Isn't their only 1 vertex angle on a triangle? I'm pretty sure that all 3 angles aren't vertex angles. Also a good way to explain it is

Sine = Opposite/Hypotenuse
CoSine= Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

A vertex is a meeting of one or more points, I believe. But your explanation is good when you are trying to find the sine etc. so it doesn't confuse people.


But still, this isn't a substitute for a google search.

Argh I was making one of these…. anyways good job ;).

EDIT: Oh and your so called "ray" is actually a directed line segment which is a vector. You wouldn't want to go into vectors unless your willing my copy our most of my Trigonometry book.

Zeph, In my book that's a ray

Can't beleive you actually made a topic on this… :p
Don't you guys get this at school?
It's one of the basics of math. Maybe move to easier tutorials?

All I have to remember is
SOHCAHTOA!!!

HinT: Google it if you don't get it noob.

It's SOS CAS TOA for me :p
Sin: Overstaande / Schuine
Cos: Aanliggende / Schuine
Tan: Overstaande / Aanliggende
EDIT: Fixed Tan. :P

From: Wizzup?
It's SOS CAS TOA for me :p
Sin: Overstaande / Schuine
Cos: Aanliggende / Schuine
Tan: Overstaande / Schuine

Yeah well… I'm American so all English for me. :P
Yours is hard to remember as a single word, at least SohCahToa sounds like a actual word. (Indianish to me heh)

Edit i think you messed up on Tan, shouldn't it be; Overstaande / Aanliggende not Overstaande / Schuine?

From: Wizzup?
Can't beleive you actually made a topic on this… :p
Don't you guys get this at school?
It's one of the basics of math. Maybe move to easier tutorials?

Actually it's needed…for me…i read it but still can't understand nothing, maybe someone make example script and tell where can it be used…

[offtopic]Do you know fat is my 9th class math???


6 pages, 3 or 4 of them filled, mostly drawing… i slept those classes, when exams were coming then my mom hired me a teacher, i learned all basics in 3 or 4 weeks, including pythagaros theorem, but not sin, cos, tan…exam mark was nearly 4[in my country there is 5 point system][/offtopic]
edit: Thx robot

From: Bobarkinator
Zeph, In my book that's a ray

Directed line segment for me. :D

But thats a ray! The American Government has been kind enough to shorten it to a three letter word! Oh wait.. Your an Aussie.. That explains the strangeness. (:p)

But Wizzup? doesn't understand. Teachers speak a different language that students only catch bits and pieces of.

I just started trig in school
I think we are learning it early cuz im in 8th grade (9th grade math though :p)

anyways, im not sure why the sin of an obtuse angle is the same as its supplement. Does anyone want to explain it to me?

Wait. You mean the sine of an obtuse angle is the same as the sine of its supplement?

Its because (I think) for obtuse angles, you end up doing the math with its supplement anyway. (Thats what I read, might not be what you've learned). I think theres some quirks in the functions that don't allow something or default to something.

I looked it up, didn't get much.

Haha, we have to use SIN, COS, TAN for Physics and graphing Vectors. We did that in Chapter 1 though. I better restudy. I forgot and exams are coming up in a month.

Mention that it only works with a trianlge that has at least one 90 degrees corner.
Otherwhise you need this:


and

We havent had this in school yet >_<'.
So a small "head start" for me.. :P

I don't take trig so I don't think I need a huge background in it.

I take Geometry, Algebra II, Pre-Calc, AP Calc for HS. I'm in Geometry right now.

From: Wizzup?
Mention that it only works with a trianlge that has at least one 90 degrees corner.
Otherwhise you need this:


and

Wait… what was 2R again? I don't recall that in the equation when I was in school.

And the first equation… BLAH lol, I rather stick with second one.

From Wikipedia:
[BANANA]where R is the radius of the triangle's circumcircle. [/BANANA]

Well in some situations you can only use the Sine Law, and in others you can only use the Cosine Law.
Use the Cosine Law when

* the third side of a triangle if one knows two sides and the angle between them


* the angles of a triangle if one knows the three sides


* the third side of a triangle if one knows two sides and an angle opposite to one of them

Taken from wikipedia, so visit it for more information. :p

From: Wizzup?
Mention that it only works with a trianlge that has at least one 90 degrees corner.

It's possible to have a triangle with more than one 90 degrees corner? :-P

Also, you might want to include stuff about circles and radians in your tutorial, would make it a much better tutorial :)