Trigonometry “basics”

[stiff plover]

Proof that sin^2+cos^2=1

[brittle pike]

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[blazing horizon]

Take a right triangle with a hypothenuse of length 1 then consider an angle of the triangle (call it x) then using trig in the right triangle (cos(x)=adjside for instance)and the Pythagorean theorem you can deduce the formula

[stiff plover]

wdym

be specific thanks

[stiff plover]

but where is sin thehta

[blazing horizon]

Well sin(x)=oppside here

In general cos(x)=adjside/hypothenuse and sin(x)=oppside/hypothenuse and using the Pythagorean theorem what’s cos^2(x)+sin^2(x)?

[stiff plover]

i don’t understand u

[round kestrel]

@stiff plover Θ (theta) is a variable that is customarily used to mark angles whose dimension is unknown, or irrelevant for the purposes of exploring the behavior of functions

Θ can be 2.5, 45, 212.5, whatever

Θ = x

It's just a variable name

[jade pilot]

Do u know soh cah toa?

[brazen crescent]

Now square both of these, add them, and use the pythagorean theorem whenever u can @stiff plover

[sage chasm]

Romans 12:19

Romans 12:19

[round kestrel]

I'm not a huge fan of the Greek variables, but at least they tend to have very specific meanings

[brazen crescent]

did you know?! pi may also be used as a variable and it's completely legal and even euler did it

[round kestrel]

Dear Lord, I'd flip a table if someone started getting shifty with standard identifiers like that

[brazen crescent]

lol euler used pi for any circle variable he needed to solve a problem in his works, anyways this isnt the right channel for this discussion, #geonosidan-prison-complex probably is

[coarse quiver]

Lol yeah

[brazen crescent]

this is just... not general

[coarse quiver]

wym

[brazen crescent]

you assumed the hypotenuse is 1

[coarse quiver]

I didnt assume its one I set it to be one

[brazen crescent]

i mean to not lose generality you should take it to be H

[coarse quiver]

im just showing him where it came from

[brazen crescent]

that is NOT where it came from

[coarse quiver]

well thats one way of deriving it

[brazen crescent]

no it isnt

[coarse quiver]

how lol

[brazen crescent]

that only derives it for right triangles with hypotenuse being 1

what about all the others

[coarse quiver]

yeah

mb I didnt indicate the right angle

lol

[brazen crescent]

doeesnt even matter that is nto the problem

the problem is if H isnt 1

[coarse quiver]

Well I just set the hypotenuse equal to 1 to simplify it

it doesnt really matter

because itl cancel out regardless

[brazen crescent]

that loses generality but i wont yap about it here anymore

[round kestrel]

The point I think Romans is trying to make is that this is only valid on the Unit Circle, which is generally not applicable to most right triangles students will encounter.

I can't begin to tell you how infuriating it is when I try to utilize a basic generalization, but either all the variables aren't defined, or there is a consistently present variable (such as the length of the hypotenuse) that is missing.

Humans are very, very good at pattern recognition. The point is to provide the best possible pattern for students to follow.

[coarse quiver]

Fair enough

[little umbra]

several ways to do this

[stiff plover]

thank u so much for explaining it by drawing 🙏🏻😊

[versed nest]

@stiff plover has given 1 rep to @coarse quiver

[stiff plover]

+close