My brain just cannot understand trigonometry

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PokeJoe: Aug 24, 2004; hail cgatan

I never understood this stuff intuitively either until I saw a bunch of the gifs like these posted back in the day

# ? Jun 3, 2022 07:08

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# ? May 7, 2024 05:40

Elentor: Dec 14, 2004; by Jeffrey of YOSPOS

Nooner posted:

Who the gently caress needs to know math lol

I'm a technical artist which is possibly the job with the least descriptive name ever.

All I do is linear algebra, trigonometry and general assorted math that everybody else is absolutely sure they wouldn't need to use after school.

# ? Jun 3, 2022 07:11

Methanar: Sep 26, 2013; by the sex ghost

Cubone posted:

trig identities were fun in integral calculus, though, they're like little logic puzzles

basically, except the fun part. For a while I wasn't even thinking of some of these problems as being math, as much as bullshit puzzles where I know there's some answer if I just twist all of my little formulas and tricks in the right way.

I didn't understand a god drat thing, I just barely knew enough about my tools to fake my way through.

# ? Jun 3, 2022 07:12

Big Scary Owl: Oct 1, 2014; by Fluffdaddy

Rock Paper Tongue posted:

At their core, sine, cosine, and tangent lines are all ratios, as someone mentioned earlier. Let's start with a basic triangle:

It's got three sides, as triangles do. A horizontal base, a vertical height, and an angled hypotenuse, plus all the angles made from where the lines meet. In this case, we want to do some digging and see if we can figure out a pattern for that angle in the bottom right, maybe relate it to some of the other values in the triangle. To make the sides we're talking about clear, let's label those sides relative to the angle in question, which we'll call theta:

Alright, so we have theta, the HYPOTENUSE, the side OPPOSITE theta, and the side ADJACENT theta. Hypotenuse is h, opposite is o, adjacent is a. That's all well and good so far, but we don't have anything to really derive yet. What we can notice here, however, is that there's an infinite number of triangles that we can draw, all with different side lengths, but with the same value of theta:

Notice that the opposite and the adjacent need to change by certain amount each, in order to preserve the value of theta. In the above triangle, we can see that increasing a by two squares means we need to increase o by one square to keep the angle the same. What we have now is a ratio, the amount that one side needs to increase relative to the other in order to preserve that angle. And if we look a little closer, we can actually find that all of the sides of this triangle need to maintain a certain ratio to preserve the angle; let's give these ratios names to make it easier to identify them, and let's explicitly say which ratios we're taking when we talk about them:
sine(theta) = opposite / hypotenuse
cosine(theta) = adjacent / hypotenuse
tangent(theta) = opposite / adjacent

For any given angle of theta and a single side measurement, we can now derive the dimensions of the rest of the triangle, and all because triangle sides and angles have a very rigid relationship. If we were to simplify this and make sure that our side values are capped at one, we can draw what's called the unit circle:

What does all of this show us, and how does it relate to a circle? Well, if we have a line length of 1, and we set it at some angle theta from the horizontal axis, we can derive the sine, cosine, and tangent from it pretty easily, since we always know the length of the hypotenuse. One neat thing about the unit circle is that for any given angle of theta, the cosine of that angle is the value of the horizontal line, while the sine is the value of the vertical line.

If we were to chart the sine and cosine of each value of theta, all around from 0 degrees to 360 degrees, we'll notice a few things.
One, we notice that they are periodic; a 0 degree angle, a 360 degree angle, a 720 degree angle, and so on will all have the same values. If you keep increasing theta, you'll get the same graph no matter how far out you go.
Two, we notice that they hit a maximum at 0, 90, 180, and 270 degrees. Those angles give us a cosine of 1 at 0 and 180 degrees, and a sine of 1 at 90 and 270 degrees, which is the highest that those values can reach. We can't go lower than zero, and we can't go higher than 1.
Three, we notice that cosine takes on the exact same values as sine, just at different angle measurements. Sine is the exact same graph as cosine, only shifted along a little bit. Skinner posted this gif that illustrates it pretty well:

We can use this to turn a sine value into a cosine value at a different angle, which comes in handy for certain substitutions and proofs.

You can take this further into the complex plane, and do some crazy poo poo with euler's theorem to relate sine and cosine to the square root of negative one, which has some far reaching effects in things like discrete number theory and electrical engineering. Trig is some baller poo poo, it's fun, it's super useful, and I loving love it.

Holy poo poo thank you very much for the effortpost! So as cosine basically correlates to the horizontal line and sine the vertical one as you mentioned, what would the tangent be in this case? I know about that the tangent relates to the circle, but I don't see how it relates to the triangle or what it's used for.

# ? Jun 3, 2022 07:56

Jaguars!: Jul 31, 2012

Tangent is how the two sides of the triangle that connect with the right angle compare to each other. So as above, to get it you just divide the opposite side / adjacent side. If you're trying to place it on the circle, it is literally a tangent, which can be seen on some of the animations people have posted. If you do the whole "Increase the angle to see what happens" thing then it follows a weird pattern that becomes useful once you move to stuff that's more ambitious than just right angle triangles.

If you have a look back to the formulae on Schweinhund's picture and have a really good look you realize how simple trig ratios are. They aren't arrived at by complicated poo poo, it's literally dividing one measurement by another. The x scare people because they think of algerbraic rearrangement but it's just there because it represents the angle of the particular triangle you're working on.

# ? Jun 3, 2022 08:25

CaptainSarcastic: Jul 6, 2013

Math? No thank you.

Highest level math I ever took was pre-calculus in undergrad, and I barely managed to scrape by. Even then it was only thanks to a really good instructor I was able to grasp it as well as I did. So, kudos to good math teachers, I guess.

# ? Jun 3, 2022 09:17

Ralph Crammed In: May 11, 2007; Let's get clean and smart

I just spent half an hour trying to figure out the descripency between one of my timesheets being 9 hours when I added it up but working out to be 10 hours when I did the math for my invoice, so don't talk to me about *cosines*.

# ? Jun 3, 2022 09:19

Private Speech: Mar 30, 2011; I HAVE EVEN MORE WORTHLESS BEANIE BABIES IN MY COLLECTION THAN I HAVE WORTHLESS POSTS IN THE BEANIE BABY THREAD YET I STILL HAVE THE TEMERITY TO CRITICIZE OTHERS' COLLECTIONS

IF YOU SEE ME TALKING ABOUT BEANIE BABIES, PLEASE TELL ME TO

EAT. SHIT.

Cubone posted:

I learned trig over a weekend and tested in to precalculus
which was basically the same as not learning trig, because you're not going to retain something you learn over a weekend

unless it's, like, whistling

so when I went on to higher math I had to basically go back from time to time like "gently caress gently caress gently caress what the gently caress is the unit circle"

and from what I remember the unit circle is the best thing in the universe?
if you can remember like 40% of it you can extrapolate the rest on a piece of scratch paper, and it has just about everything you need to know just on it (as long you remember cosine is at the x coordinate and that tangent is sine/cosine, but if you don't remember that both can be derived from knowing why the unit circle works and, just, soh cah toa)

I don't even really think of trig functions as being relationships between angles and length anymore, primarily, to me sine is a wavy line oscillating between 1 and -1 whose intercepts and inflection points are all proportional to pi and if you're ever in doubt about when that is, muhfuckin unit circle

trig identities were fun in integral calculus, though, they're like little logic puzzles
that might be the geekiest thing I've ever said but it's true, it's weirdly satisfying using them to crack open a problem
if you know them at a glance you can be like (this is an extremely basic example because I haven't been in a calc class in years please do not make fun of me) ok well
sin²𝑥=�(1-cos2𝑥)
so
∫sin⁴𝑥d𝑥 = ∫(�(1-cos2𝑥)��(1-cos2𝑥))d𝑥 = � ∫(1-cos2𝑥)(1-cos2𝑥)d𝑥 = � ∫(1-2cos2𝑥+cos²2𝑥)d𝑥
and
cos²𝑥 = �(1+cos2𝑥)
means
cos²2𝑥 = �(1+cos4𝑥)
which means
� ∫(1-2cos2𝑥+cos22𝑥)d𝑥 = � ∫(1-2cos2𝑥+�(1+cos4𝑥))d𝑥 = � ∫(1-2cos2𝑥+�+�cos4𝑥)d𝑥
and since
if f(𝑥) = g(𝑥)+h(𝑥) then ∫f(𝑥)d𝑥 = ∫g(𝑥)d𝑥+∫h(𝑥)d𝑥
that means
� ∫(1-2cos2𝑥+�+�cos4𝑥)d𝑥 = �(( ∫1d𝑥)-(2∫cos2𝑥d𝑥)+(∫�d𝑥)+(�∫cos4𝑥d𝑥))
which is obviously equal to |�(𝑥-sin2𝑥+�𝑥+⅛sin4𝑥)+c|
and since you're in a calculus class you can just stop there because your high school math teachers lied to you, nobody gives a poo poo about simplifying your answers

no I have not used any of the math they made me learn for my computer science degree
but I'm glad I learned it
I'm glad I know how to solve optimization problems, mostly
but maybe some day somebody will hire me to do something with, like, spherical harmonics
and I'll be like

AHHHHHHHHHHHHHHH 😱😱

because I didn't learn that

I've gone through basically all this myself and up until the last bit you've mentioned it was fine and everything (except that I actually knew what unit circle and eurler's theorem were before uni), but then you get into working with data in more than 3 dimensions and/or linear algebra where the matrices have sines/cosines in it and I just, I got lost. And yes I know it's applicable to computer graphics.

Still managed to get a 2:1 and everything.

But I'm not a huge fan of trig since then, was pretty much the only thing I struggled to understand throughout university.

Private Speech fucked around with this message at 09:39 on Jun 3, 2022

# ? Jun 3, 2022 09:33

Mooey Cow: Jan 27, 2018; by Jeffrey of YOSPOS; Pillbug

Big Scary Owl posted:

Holy poo poo thank you very much for the effortpost! So as cosine basically correlates to the horizontal line and sine the vertical one as you mentioned, what would the tangent be in this case? I know about that the tangent relates to the circle, but I don't see how it relates to the triangle or what it's used for.

If you have your point (x, y) on the circle, then the tangent is simply the slope of the line that goes through that point and the origin.

Like you have your line equation y = k*x, so if you know x and y, then k = y / x. If they happen to be on a circle (ie satisfy x^2 + y^2 = 1 (in this case the circle can have any radius since it's a ratio)), then k is the value of the tangent function.

Thus you get the equation tan a = sin a / cos a

# ? Jun 3, 2022 10:14

Songbearer: Jul 12, 2007; Fuck you say?

It's what makes you good at Worms Armageddon which is an important skill

# ? Jun 3, 2022 10:32

Jestery: Aug 2, 2016; Not a Dickman, just a shape

I have been helping a Deaf student with some trig stuff lately with an assignment relating to football and kicking angles

Mathematical conversation is not a strong suit of signed communication and I ended up building a scale model so we could actually point at datums and draw lines on stuff

Was really good fun

# ? Jun 3, 2022 11:06

Lil Swamp Booger Baby: Aug 1, 1981

Swagonometry

# ? Jun 3, 2022 11:24

GABA ghoul: Oct 29, 2011

I don't know a single person who got laid by taking the sine. It's completely useless stuff

# ? Jun 3, 2022 11:40

Mooey Cow: Jan 27, 2018; by Jeffrey of YOSPOS; Pillbug

Angles are for dumbasses

# ? Jun 3, 2022 11:48

Jestery: Aug 2, 2016; Not a Dickman, just a shape

Mooey Cow posted:

Angles are for dumbasses

Lol if you can't radian

# ? Jun 3, 2022 11:55

Samuel L. Hacksaw: Mar 26, 2007; Never Stop Posting

Lol get that tongue tangential to my bawls b*ych

# ? Jun 3, 2022 12:02

SniperWoreConverse: Mar 20, 2010; Gun Saliva

Chinatown posted:

ive forgotten basically all math i was taught as a child including long division

we have computers now

same. I think i still remember fractions and maybe can multiply if i count on my hands

# ? Jun 3, 2022 12:30

necroid: May 14, 2009

Cubone posted:

which is obviously equal to |�(𝑥-sin2𝑥+�𝑥+⅛sin4𝑥)+c|

yes

# ? Jun 3, 2022 12:41

necroid: May 14, 2009

read this thread p high while bored out of my mind working and oo weee

# ? Jun 3, 2022 12:42

Randarkman: Jul 18, 2011

The best math is the type where there are no definite numbers and you don't need to use anything other than a pencil and some paper.

# ? Jun 3, 2022 12:45

Speleothing: May 6, 2008; Spare batteries are pretty key.

Unit circles and waves are unnecessary bullshit. Trigonometry is for building roofs.

# ? Jun 3, 2022 14:10

BAGS FLY AT NOON: Apr 6, 2011; A Soft Nylon Bag

In my job sometimes I need to add two or possibly three amounts together, and occasionally subtract an amount from a total.

# ? Jun 3, 2022 14:17

Mooey Cow: Jan 27, 2018; by Jeffrey of YOSPOS; Pillbug

If i had a job, i'd quit

# ? Jun 3, 2022 14:36

DrPossum: May 15, 2004; i am not a surgeon

the plural of abacus is abussy

# ? Jun 3, 2022 14:39

frumpykvetchbot: Feb 20, 2004; PROGRESSIVE SCAN; Upset Trowel

Write a raytracer from first principles, OP. It will come back to you.

# ? Jun 3, 2022 15:38

GABA ghoul: Oct 29, 2011

First principles? I can't even write one from second or third ones

# ? Jun 3, 2022 15:43

EorayMel: May 30, 2015; WE GET IT. YOU LOVE GUN JESUS. Toujours des fusils Bullpup Fran�ais.

If this thread was posted in 2005 OP probably would've been banned for a homework help thread by ozma/debbie metallica

# ? Jun 3, 2022 15:51

Mozi: Apr 4, 2004; Forms change so fast
Time is moving past
Memory is smoke
Gonna get wider when I die; Nap Ghost

fun fact: Sarah Palin named her son Trig because she is a huge fan of mathematics

# ? Jun 3, 2022 16:47

Oldstench: Jun 29, 2007; Let's talk about where you're going.

The first time I took acid I peaked during geometry class. Math has been confusing and weird to me ever since. I mean, I was always a dumbass, but I think that broke me.

# ? Jun 3, 2022 17:34

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# ? May 7, 2024 05:40

sudonim: Oct 6, 2005

Some good effortposts in here.

I love dingdongs who go all "Math sucks, nobody uses it," while totally taking for granted that planes aren't falling out of the sky, buildings aren't collapsing on top of them, and their electronics aren't spontaneously exploding (vapes and Samsungs aside (because someone didn't do the math)).

# ? Jun 3, 2022 19:16

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