Hell_Demon (11-02-2010),Pacciatto (11-04-2010)
Okay so, this is going to a quick Trigonometry lesson it will explain Sine, Cosine and Tangent. (Not the inverses of them)
This tutorial will only be going over basic solving, only one method of solving each trig equation/problem.
This tutorial also assumes you have a prior knowledge of angles and degrees.
First off, let’s start off where we can use these: Right triangles.
A right triangle is any triangle with one of its angles being exactly 90 degrees, the lengths and other angles don't matter, we will be using trig to find those out.
Here is an example of a right triangle:
First thing we'll learn is how to label our triangle accordingly. There are 3 labels to put on the sides of our triangle, the first of which, that will always be the same is Hypotenuse (high-pot-en-oos) abbreviated Hyp. This will ALWAYS be the longest line in the triangle. So in our triangle, that is this:
The next two labels, opposite (abbreviated Opp.) and Adjacent (abbreviated Adj.) depend on which angle/side we are finding. So they will come in later.
When using Sine, we are going to be finding one of the two sides that are not Hyp. To find these we will need one angle, and the length of Hyp.
So to show this, I'll give this angle and this length:
We will be finding x.
Now to explain how Sine works, I'm going to start with the expression Sine equals Opposite over Hypotenuse
So, Sine = Opp./Hyp.
Meaning, Sine(angle) is equal to the Opposite side, divided by the Hypotenuse side.
Now, I'm sure I just fried a few brain cells, but, let me demonstrate with our example.
Back to our labeling, Opposite and Adjacent depend on which angle we are putting into our trig function. So, since we are putting the 30 in, this is how our triangle gets labeled:
This is how I came up with that, the side Hyp. will always be the longest side (gone over before), and now, we learn that the side Opposite, will always be opposite the angle we are putting in our function. In this case, we are putting the 30 into our function so the side opposite our angle, is the Opp. And the side touching is Adjacent (definition of adjacent is: touching)
So now that we have our labeling down, we can get to the hardcore problem solving.
Sine(30) = x/15
And with basic algebra we can work this out, pop sine 30 into a calculator and we get 0.5, our equation is now
0.5 = x/15
Multiply both sides by 15 and find our x value
7.5 = x
That is our answer; we have found the length of opposite.
Finding the last length can be found with Pythagorean's theorem. (Look it up, not in this tutorial)
Okay, so, hopefully you understand Sine, because we are moving onto Cosine.
Cosine is equal to Adjacent over Hypotenuse, so it's the same process as before, but this time Cosine will be used to find x in this situation:
Notice the different from before? It's a different line. Because we are still measuring the same angle, that line is Adjacent, and Cosine = Adj./Hyp.
So, let’s do the problem solving again
Cosine(30) first, this is 0.86602540378443864676372317075294 (irrational number, just round it to 3rd decimal place: 0.866)
So now we have
0.866 = x/15
Multiply both sides by 15
12.99 = x (approximately, because remember we rounded. If you want exact numbers, don't ever evaluate yourself. Like if you're doing an aimbot, you need to have all the values stored in variables and the calculations carried out from there)
That is cosine, in a nutshell.
And finally, our last function is Tangent.
Tangent is equal to Opposite over Adjacent (Tan = Opp/Adj)
And here is our example question:
Okay so, this is going to a quick Trigonometry lesson it will explain Sine, Cosine and Tangent. (Not the inverses of them)
This tutorial will only be going over basic solving, only one method of solving each trig equation/problem.
This tutorial also assumes you have a prior knowledge of angles and degrees.
First off, let’s start off where we can use these: Right triangles.
A right triangle is any triangle with one of its angles being exactly 90 degrees, the lengths and other angles don't matter, we will be using trig to find those out.
Here is an example of a right triangle:
First thing we'll learn is how to label our triangle accordingly. There are 3 labels to put on the sides of our triangle, the first of which, that will always be the same is Hypotenuse (high-pot-en-oos) abbreviated Hyp. This will ALWAYS be the longest line in the triangle. So in our triangle, that is this:
The next two labels, Opposite (abbreviated Opp.) and Adjacent (abbreviated Adj.) depend on which angle/side we are finding. So they will come in later.
When using Sine, we are going to be finding one of the two sides that are not Hyp. to find these we will need one angle, and the length of Hyp.
So to show this, I'll give this angle and this length:
We will be finding x.
Now to explain how Sine works, I'm going to start with the expression Sine equals Opposite over Hypotenuse
So, Sine = Opp./Hyp.
Meaning, Sine(angle) is equal to the Opposite side, divided by the Hypotenuse side.
Now, I'm sure I just fried a few brain cells, but, let me demonstrate with our example.
Back to our labeling, Opposite and Adjacent depend on which angle we are putting into our trig function. So, since we are putting the 30 in, this is how our triangle gets labeled:
This is how I came up with that, the side Hyp. will always be the longest side (gone over before), and now, we learn that the side Opposite, will always be opposite the angle we are putting in our function. In this case, we are putting the 30 into our function so the side opposite our angle, is the Opp. And the side touching is Adjacent (definition of adjacent is: touching)
So now that we have our labeling down, we can get to the hardcore problem solving.
Sine(30) = x/15
and with basic algebra we can work this out, pop sine 30 into a calculator and we get 0.5, our equation is now
0.5 = x/15
multiply both sides by 15 and find our x value
7.5 = x
That is our answer, we have found the length of opposite.
Finding the last length can be found with Pythagorean's theorem. (look it up, not in this tutorial)
Okay, so, hopefully you understand Sine, because we are moving onto Cosine.
Cosine is equal to Adjacent over Hypotenuse, so it's the same process as before, but this time Cosine will be used to find x in this situation:
Notice the different from before? It's a different line. Because we are still measuring the same angle, that line is Adjacent, and Cosine = Adj./Hyp.
So, lets do the problem solving again
Cosine(30) first, this is 0.86602540378443864676372317075294 (irrational number, just round it to 3rd decimal place: 0.866)
So now we have
0.866 = x/15
multiply both sides by 15
12.99 = x (approximately, because remember we rounded. If you want exact numbers, don't ever evaluate yourself. Like if you're doing an aimbot, you need to have all the values stored in variables and the calculations carried out from there)
That is cosine, in a nutshell.
And finally, our last function is Tangent.
Tangent is equal to Opposite over Adjacent (Tan = Opp/Adj)
And here is our example question:
As you can see, same angle again, but different sides yet again.
So we put Tan(30) into our calculator, and get: 0.57735026918962576450914878050196
We can round to first 3 decimal places again: 0.577
Now we have
0.577 = x/10
Multiply both sides by 10
5.77 = x
And we have our answer! =D
Now a lot of people are wondering, so how do I know when to use Sin/Cos/Tan? And how the hell do I remember which one is what?
Simple.
SOH
CAH
TOA
Just remember that basic phrase, write it down before you do any calculations.
S=O/H
C=A/H
T=O/A
That is all for the lesson, sorry if some things are unclear, I am writing this at 1:30 in the morning on a school night, no idea why.
Here are some practice problems: (~ = approximately)
Highlight this text for answer: x =~ 3.38
Highlight this text for answer: x =~ 14.3
Highlight this text for answer: x =~ 19.86
If you have any trouble, just post a reply and I'll help you out. If this was helpful though, feel free to hit the thanks button! =D
Oh and for those of you wondering, how the hell does this incorporate into an aimbot? Well think of it this way, the distance between you and the enemy is Hypotenuse, and then you make right triangle out of that and use trig to get the angle you need to aim to hit them.
Note, you wont be able to use anything learned here to get the angle, you have to use inverse trig functions, basically the opposite, instead of putting in an angle you put in the division equation of the two sides, and it gives you the angle. I may write another tutorial on this.
~lilneo
Hell_Demon (11-02-2010),Pacciatto (11-04-2010)
Good tut for starters, you practise on assaultcube as it's quite easy to get what u need there
Ah we-a blaze the fyah, make it bun dem!
Just realized, because I was writing the tutorial in the posting form, and in notepad in case of a web browser error. I somehow copy pasted the entire thing on top of itself. A mod or something want to fix? Right after I start explaining Tan, the tutorial restarts itself. Just delete the first part, from the beginning to where it restarts.
~lilneo
Missing cotangent (tan⁻¹), secant and cosecant (sec⁻¹). Also it would be useful to add some structure to the guide, to explain the graph shapes & any asymptotes and stuff /
And complex graphs <3
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Anyone who has taken geometry should know this stuff by heart. I used it in all of my physics and math classes last year. And in my AP physics and calc classes this year.
[YOUTUBE]NsOG1khq8Rs[/YOUTUBE]
^^^Check Out the Crazy Black Chick that was on my Bus^^^
You need to go deep such as sin2x= 2sinxcosx, cot=1/tan etc.
Also need to discuss more formulas such as Cos(a+b)=cosacosb-sinasinb
You say trig but I learned this stuff in geometry. I also learned the inverses in geometry so... just wanted to brag xD
I'm Alen on Steam. RIP Skype Friday nights.
I'm Navi's lover <span class="emoji-outer emoji-sizer"><span class="emoji-inner" style="background: url(chrome-extension://immhpnclomdloikkpcefncmfgjbkojmh/emoji-data/sheet_apple_64.png);background-position:2.5% 97.5%;background-size:4100%" title="hearts"></span></span>
Messenger: Toxin about Dave | Paladin on Skyrim's AI | Dakota on JB | Royku leeching | Sjoerd's penis | Blitz's derpiness | Jason on Blitz
Dave84311: God I've always wanted to eat crayons, with their vibrant colors. Only if they had taste.
Mr. Lonely: @Alen I like making you wet, it makes me hard.