What the fuck is trigonometry about...

what the fuck is trigonometry about, seriously i can't find any explanations for this and everyone is just 'dude sohcahtoa lmao' whenever i ask. i realize that is angles and triangles and shit but where do the sine/cosine/tangent functions even come from

Other urls found in this thread:

khanacademy.org/math/trigonometry
en.m.wikipedia.org/wiki/Similarity_(geometry)
sciencesims.com/simdocs/origin-sine-cosine
twitter.com/NSFWRedditGif

Nigga you can google this shit.
Sine is the y coordinate of the intercept of a circle of radius one and a line from the origin at a given angle
Cosine is the x coordinate
Tangent is Sine/Cosine (also some other shit but cbf explaining).
Google it and you'll see proofs of why these definitions work with sohcahtoa

You must be over 18 to post here. Also pay attention in class

there's like 5 threads currently with obviously underage people in them. i think i'll be fine

fucking all that got explained to me in class was sohcahtoa and degrees/radians and that was all i've heard of it for 2 years.

Where are you from?
khanacademy.org/math/trigonometry
I'd report you but I was an underage shitposter for years so I know how it feels

>where do the sine/cosine/tangent functions even come from

Measuring triangles. There's no mechanical way to figure out the sin function, you just have to keep comparing ratios and recording the results.

>where do the sine/cosine/tangent functions even come from
I find it helps to think of them more like operators than functions that have some hidden math behind them.
The sine of some angle gives you the ratio of the side opposite the angle to the hypotenuse of a right triangle. This ratio will always be true at this angle regardless of the other dimensions of the triangle.
Also make a serious effort to understand how trig interacts with a unit circle. It'll help you a lot later on - you never stop using trig

Nobody knows OP. The sine and cosine functions etc. are mathematical anomalies that appeared throughout the development of mathematics. Most people only pretend to know what they mean but the truth is that the truth is long forgotten. All we know is you can use them to measure the ratios between sides of right angled triangles.

en.m.wikipedia.org/wiki/Similarity_(geometry) This is the reason sine and cosie are well defined. It's literally sohcahtoa

Trigonometry is actually simple if you visualize it using the unit circle.

Yup thinking about it geometrically really helped drive the concepts home for me

trigonometry is just about getting acquainted with the sin and cos functions. they're that important, because they are related to rotations, a very natural set of transformations that is useful in STEM

this means you'll see them in physics and calculus classes in uni

>what is taylor series?

Good post but a more intuitive interpretation of tangent function is that it is the slope of the radius with x = cos(theta), y = sin(theta).

Kek

Sine comes from the sine function. You get them through simple harmonic motion.

sciencesims.com/simdocs/origin-sine-cosine

>what is trigonometry

It is about describing the relation between the sides of polygons.
>b-but wasn't it just about triangles?

Triangles are simply the simplest polygons. You can deconstruct every polygon into triangles and then if you assign each side of the polygon the side of a triangle then by finding relations between those triangles then you find relations about the side of the polygon (think about dividing a square unit square into 2 right triangles to then show that their diagonal is square root of 2),

> where do the sine/cosine/tangent functions even come from

After you study the sides of triangles for a while you realize that the sides of a triangle are not only related to each other, but they are also related to the angles of the triangle. Now you have a new field of study: angle-side relations, which yielded the trig functions.

Trig functions are not functions like x^2. We do not have the values they yield. But from proving some angle-side relations, we can find ways to approximate the values they would give us.

Then you can help yourself by considering only easy to work triangles (like triangles in the unit circle) to find some more general rules and to compute a table of important values that other people can use with the properties to approximate the value of all possible angles.

That is all trig is.

Veeky Forums disappoints... should have posted wildburger by now.

It's the way of calculating the ratios between two sides given the angle, so therefore if you know one side (the hypotenuse) is "x" cm long, and the angle is "theta" then the ratio between x and the other side (the opposite side to the angle), which we can call "y", is equivalent to the sine (which is just the function to work out the ratio) of the angle, and thus y must equal x sin theta.

For me, it was the thing that ruined geometry class
>assigning numeric lengths to things
>making me pull out my calculator
>took focus away from proofs to plug and chug

can someone show how to calculate sin(1)

i find i hard to understand the functions without ever seeing what they actually do

1 - (1^3)/3! + (1^5)/5! - (1^7)/7!...

Wow, even wikipedia

Are you familiar with the Pythagorean theorem?

It's about the relationships between angles and sides of triangles based on the relations between the sides and angles of a right triangle inscribed in a circle with radius 1

>trigonometry
trigonon ("triangle") + metron ("measure")
yes, it's that simple

Where is arccohavercosine?

Imagine P walks around the circle
picture how does that affect the angle, the sine, the cosine, the tangent

Use the unit circle and everything will be clear

you still have to compare triangles to get the derivatives, although you don't do it everytime