Sup /sci/
I am experiencing difficulty learning Trigonometry for the first time. I am currently working on graphing sin/cos/tan functions as well as inverse functions. Hit me with your best information and insults.
>>7890823
Lurking because I'm in calc III and I still don't fucking understand trig.
try it with tau
>>7890828
You give me hope. Even the tutors at my school teach trig with ridiculous apprehension.
sohcahtoa
>>7890828
I'm in calc 3 as well, and I'm not quite sure - what's there to understand? Isn't it just triangles and their side lengths?
>>7890911
I don't do well with straight memorization. Things go exponentially smoother when I understand what I'm learning. I do not know what sin is. I do not know what tan is. I do not know what secant is. I know when they are used, I know the relationship between them, but I don't understand what Sin pi/2 is. To me they're just arbitrary operations with no real meaning behind them that I plug into an equation, and so I struggle when I actually have to evaluate a trig function.
>>7890928
try it with fucking tau
>>7890828
Studying analysis in 4th year of an honours math program and I don't really get trig. I mean I get it, but it's not all memorized. Like if I need to know arccotan(0) it's gonna take me a while and a lot of triangles to figure that out
>>7890932
i dont think any triangles are going to help you find a number that doesnt exist
cotan(0)=cos(0)/sin(0)=cos(0)/0
>>7890928
OP here. Thank you for posting literally word for word what ive been thinking since the semester started.
>>7890931
>>7890893
I don't know what you mean by this.
>>7890932
I'm not saying I want to work out trig calculations by hand everytime. I can memorize facts easily if I understand them. If I don't then it lasts about 2 days in my head. If I have a concept of how something like cosine works, then I can actually memorize it's properties more efficiently. Otherwise I'm doing trig problems every other fucking day, whether it's relevant to the section or not, which I think you can agree is incredibly inefficient and tiresome.
>>7890928
>I don't do well with straight memorization
remember OP, Some People Have Curly Black Hairs Through Proper Brushing
i dont get the question.
they are just ratios.
>>7891191
no sweat you mongoloid
>>7891206
no sweat dude just enjoy it, way better than hammering in your neurons a godforsaken load of terrible formulas that don't make sense neither are beautiful except for a few cringeful people who think only cringeful people can find math awesome and interesting and not in the cringeful way
it's not an easy task using tau but is a less traveled one and you gain the gift of not being obsessed with cringeful pie jokes
>>7890823
Same boat OP. Been drawing Unit Circle as much as possible, watching videos, trying to logic out all Sin/Cos/Tan functions as I go. It's lots to take in.
>>7891216
How does Tau work out when you start getting in to some basic algebra? I see that its equal to (Pi X 2) but are there any points where Tau wont work?
>>7891216
>doing trig with tou = 2*pi
is this a new meme?
>>7891233
yeah, the point is right there. you see they are right when disphits like this one >>7891247 start to spout their dumb, let-me-defend-my-braindead-brainwash-education shit.
>>7891245
just like that. tau is 2pi. you can go on from there and if your teacher is an asshole you just convert back to pi so he/she/it can be happy thinking you're another idiot who thinks that can learn their golden truth instead of repeating the damn formulas and doing the same thing over and over again like you're supposed to do.
trig should make sense. you can't just memorize the damn thing, you need to understand it because it is that important but the bastards just smile and wave "you don't need to know all of this, unless you already know you're a genius then" "oh e to the i times pi plus one is zero the beautifulest thing is my favourite i love euler"
pi drags the thing to minus one. it cloaks the damn thing is turning. but brainwashed idiots will defend it because it's tradition. it's too old to be defied.
then a dude finds the fucking newton's book had an error centuries after that virgin kicked the bucket. i want the people who treats knowledge as sacred to be fucked with a rusty fencepost.
to defy is the very breath and blood of the thing and yet they want us to eat it dead and discourage us to hunt it. dayum shame.
>>7890823
Pic related: the only triangle you need to memorise to do non-calc trig
big angle opposite big side, small angle opposite small side.
>>7891233
again, see the kind of people that I refer when I say that simply memorize shit and then spout that everything else is wrong?
like this idiot >>7891308
there is a new thing, it might blow up your head son, tau radians = 360° so a fucking ratio of fucking radians can make sense instead of half-turns in a full circle
>>7891308
On the unit circle a full revolution is two pi radians. This triggers some people for some reason. I believe it has to do with making divisions of two pi. When you use tau you are diving the unit circle into sections and one full revolution is one tau. It is totally arbitrary which you choose.
>>7891319
>2016
>still using degrees
the babylonians were smart. they knew 360 was a good number. any mouthbreathing drooling idiot knows if you do a 360 you do a turn and then end in the same position.
They envy them. Like this guy >>7891324 as they can't (or they don't want to) convince people that 2 pi is cooler than that. so them eggheads keep your pies in your good, comfy ovens.
tau is coming to teach people that trig is for everyone.
>>7891216
Just memorize the first quadrant. you can find the others just by subtracting from pi, adding to pi or subtracting from 2pi
>>7891329
>tau is coming to teach people that trig is for everyone
trig is already for everyone. 99.9999% of people who needs to know trig can learn it the conventional way without any trouble. No ones gonna bother changing all the books just to reach that .0001%.
trig is literally the easiest branch of math. I suck at math and even I never had the slightest problem understanding tirg.
>>7891329
>>7891329
Well, two pi, or tau if you insist, is a more natural measurement of angles. It allows for the measurement of angles be based upon something more concrete than, "one turn is 360." Instead, it relates angles to the arc length of a circle. All mouth breathers know that the circumference of a circle is 2πR. It is similar to using the notion of a circular clock to communicate angle. Ever hear someone say, "On your six," to mean right behind you?
>>7890823
Key facts:
1. Sin, cos and tan are ratios of two sides in a right angle triangle. Sin is DEFINED as the ratio between the side opposite the angle, and the hypotenuse of the triangle
2.These ratios depend only on the angle between these two sides, not the LENGTH of the sides. (this only holds true for right angled triangles)
3. So, for example, when you calculate sin(30) in this triangle >>7891315 you are calculating the ratio between the opposite side and the hypotenuse. Since it is a unit triangle, you can see that this ratio is 1/2. No matter what the side lengths are, as long as it is RIGHT ANGLED, Pythagoras' theorem will apply and the ratio will be the same
4. If the ratio is always the same for an angle, then if you know the ratio, you can find the angle. This is how inverse sin/cos/tan work. Lets say oppose = 1, hypotenuse = 2. The ratio is 1/2, so inverse sin(1/2) is simply your calculator checking what angle corresponds to that ratio
5. Use the unit circle to remember when sinx/cosx/tanx are positive (top right quadrant: all are positive | top left: sin is positive only | bottom left: tan is positive only | bottom right: cos is positive only) (obviously bottom right means between 270 deg and 360 deg, top left is between 90 deg and 180 deg etc)
>>7891334
NO YOU MEMORIZE THIS YOU FUCKING IDIOT GET YOUR PI AND INSERT IT INTO YOUR ASS AND DO A FUCKING FOURIER TRANSFORM FOR ALL I CARE
dude, just leave the people who want to learn alone. you're damaged, you've been grafted this pi stupidity and are beyond repair. YOU'LL REPEAT TO THE LAST OF YOUR DAYS THAT'S THE ONLY WAY TO LEARN TRIG.
and that's terrible and sad.
>>7891340
good for you chumps, nice knowing the old way still does it right for everyone. woo go tiger
>>7891341
nice thing you've remembered that a clock uses the same babylonian system chump. it's numbered from 1 to 12 right? each hour the arrow goes on 30° or tau/12. six hours, 6 tau/12,hey, it's half of a circle! whoo! or is it pi?
a full circle is a full unit. using half a thing to describe one thing is dumb. using two times a thing to describe a thing is dumb.
when a mouthbreather wants to point directions using a clock notation he will ignore the measure of circumference all along but damn circumferences are cool. that's why we divide them by the radius and find tau.
Riddle me this:
How brain damaged do you need to be to find calculating with tau easier than with pi
If I ask you to turn 95 degrees into radians:
95 degrees = pi/2 + pi/36 = 19pi/36
or
95 degrees = tau/4 + tau/72 = 19tau/72
Show me how tau is better
>>7891349
Hi Phil
>>7891363
isn't he a cool dude, not afraid of smashing his own dick with a mallet?
you've already done it. good for me, I'm sleepy, if I had to think it would be a lot harder.
you can plainly see and show that a fourth of a circle (in radians) plus 5/360 of a circle (in radians) equals to that nice sexy prime number there. tau is there for that. you can see what's going on without coding in halves. 95/360 degrees = 19/72 radians. BRAVO DUDE YOU SURE TOLD ME PI IS BETTER
>>7891376
i'm not phil but hi
>>7891386
What's the area of a circle using tau instead of pi? Proof tau is inferior.
>>7891386
You are a fucking moron
If you can instantly reduce 95/360 into 19/72 then why the fuck are you even thinking about tau?
Tau supposedly makes trig easier for retards, and guess what, retards are dumb, that's why they're struggling with trig
What I'm saying is that tau does NOT in fact make trig easier for retards
>>7891402
lol dude for real, this is becoming embarrassing, but well, let me try, could you use pi with diameter instead of radius? because you know, pi is the circumference divided by diameter, but they sweep under the rug that detail because people are too stupid and a factor of two isn't important and in reality we measure the diameter and ignore the radius blah blah blah...
pi r squared is in fact circumference divided by diameter times half the diameter squared.
oh but it is so tidy why not use it anyway?
because then you obscure the reasoning they had to do when trying to do this shit in the past.
we know the damn area of a triangle is half its base times the height. their reasoning was to cut the circle in these thin thin triangles and mount until the circle resembled a weird-shaped form.
today we smart people call that shit a integral oh so smart we are naked monkeys dohohoh
seriously half the circumference divided by the radius times the radius squared is awesome. it becomes a damn clue to what comes next. gravity and all that juicy stuff uses that subtle power rule.
why we think people are so stupid that they would not understand it before and them slam them with it so we can look smarter than them?
>>7891413
and you are a retard because you lack the mind of a person that doesn't know trig and at least knowing what a damn fraction is, to know that radians are simply portions of a circle. portions of a damn full circle. not portions of a half circle.
>>7891422
boy, you sure would like my engineering class, where instead of radius, all the formulas use diameter/2
r^2 = (d^2)/4 all day.
>>7890823
OP, what level of math are you currently in? When I was taking trig, it was kind of stapled on to the end of the syllabus for 3 years. Algebra2/trig, Geometry/trig, then Algebra3/trig. I ended up learning it by stapling it to a rock and bashing it into my skull, but it all makes sense to me now. It was the constant repetition in physics to find angles or side lengths that taught me.
If you are in Geometry or higher, I suggest looking at the Law of Sines and figuring out why it works, that is when everything clicked for me.
>>7891453
yeah, I heard that before. and dude, if it makes sense, you don't need to rote memorize it, because it will become true even if you try it other ways. you measure the fucking diameter and then they spew the "oh but pi r squared is easier" as if we wouldn't divide the damn measure.
but anyway, each one to its own. i hope OP learns, one way or another. I'm here just to cause some ruckus, or else the thread would be another sad stupid teabagging one where people recite their prayers to their science gods and scream blasphemy to the nonbelievers.
>>7891422
>and you are a retard because you lack the mind of a person that doesn't know trig
That makes you the retard you braindead fuck
You have given literally no arugment as to why tau is better than pi apart from some autistic 'portions of a damn full circle' bullshit
What you are saying is that you, and retards like you, are too braindead to understand that 2pi is a circle
>>7890823
underage
>>7891349
> a full circle is a full unit
what's the area of a unit circle in terms of tau then?
>>7890823
He's taller than me
>>7891497
you people just love "autistic" insults huh?
okay, keep you pies kid. keep your memories intact and keep thinking it is the only way to learn it. "understand" that a full circle is two "fundamental" units is stupid and you should feel ashamed of saying that.
>>7891650
half the circumference divided by the radius.
or tau/2. isn't that a bit obvious?
>>7891987
Where did I say it was the only way to learn trig?
I'm asking you to explain to me how tau is better
And you clearly can't do that
(because it isn't)
>>7892095
and you clearly can't understand
(because you're an idiot) ^_^
>>7891315
Also worth knowing √3 ,2 ,1 Triangle as Well for the 60 ° and 30 °
>>7890928
If you want them in a actual observable form, you get them like they are in pic related.
They are just important virtual values that are implicit on the angles in geometry, thus you can find/use them in any equation that is sensible to angular geometry.
>>7892427
Sorry, I forgot my pic.
>>7890939
>when anon is this fucking retarded
>>7890939
You must be 18+ to post.
>>7890823
>tfw your daily outfit is a meme
stop copying my style neurotypicals
Here op http://mecmath.net/trig/trigbook.pdf
You can finish this In 2 weeks
>>7890823
soh cah toa
Sin=OP/HYP
Cos=ADJ/HYP
Tan=OP/ADJ
>>7890823
You don't understand trig, but you're in calc. Suck a huge fucking dick. Everyone and their fucking grandma should know that you can get the angles of any right triangle that a side of 1 by using my favorite formula of all time,
[math]f(x) ~ (0.01745329251) * arccot (x)[/math]
If you punch that into Desmos, you will get a line where x = 2 and y equals my favorite number of all time,
[math]26.565051177990099[/math]
Which is the isometric angle, commonly misplaced with 30 degrees. A 2/1 triangle has a side lengths, 2, 1 and 2.223fuckyousqrt5, and angles 26.57, 90 and 63.43.
>>7893887
fuck, may have made a miscalculation, the 0.07 or whatever was supposed to be pi/180 but that's for degrees to radians, I want radians to degrees so it would be 57.2957795131. Again, sorry. Keep in mind that I taught myself trig.
>>7891363
It's more intuitive with tau because you 0.263888..., which is just over quarter, so a right angle and a bit. It makes more sense and is easier to visualise
19pi/36 means nothing to me, nor does 1.658 rad
>>7893941
it's 0.5277pi rad which is just over .5pi rad, so a right angle and a bit.
>>7893955
True, but when you include pi it becomes less intuitive, especially for non-mathematically inclined people
>>7893965
your tau calculation also has tau in it. it's 0.263888tau rad.
>>7890823
But that's early high school stuff.
Don't they teach trigonometry in schools in US?
>>7893981
Just 0.263888... Tau. If you know 1 tau is a full circle 0.26388.. Makes more sense
