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/sci/ - Science & Math

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5670801 No.5670801 [Reply] [Original]

well /sci/ it's been about 7 years since i've taken trig and it's been 5 years since my last math class (calc 1 for science majors) how the hell do i simplify this. i've forgotten too much

>> No.5670813

please /sci/ i'll draw something nice for you if you explain

>> No.5670818

>>5670801
>>5670813
It does work; you are on the right lines.
I am trying to work it out; give me a moment.

>> No.5670824

>>5670818
thanks /sci/entist

>> No.5670863

>>5670824
Sorry, I am struggling with this. It has been a long time since I have done maths of this kind.
Hopefully somebody else can help, but I will still try.

>> No.5670892
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5670892

>>5670801
break your isoceles triangle up into 2 right triangles. the top angel splits into 15 deg.

use SOH CAH TOA
sin(15) = (a/2)/2; 4 sin(15) = a

remember your angle addition formulas.
sin(A+B) = sinA*cosB+sinB*cosA
sin(15)=sin(45-30) = 1/sqrt[2] * sqrt[3]/2 - 1/2*1/sqrt[2] = (sqrt[3]-1)/(2*sqrt[2])


a = 4sin(15) = 4 (sqrt[3]-1)/(2*sqrt[2]) = sqrt[2] (sqrt[3]-1)

pic related

>> No.5670907

>>5670863
thanks for your effort

>>5670892
brilliant. damn i miss math
thanks so much

>> No.5670908
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5670908

>>5670801
you got sqrt(8-4*sqrt3)
i dont hav the terminology so dnt laugh at my explanation: introduce the "4" under the sqrt so you get
sqrt(8-sqrt48) than apply the formula i uploADED

>> No.5670922

>>5670908
>implying anyone knows these formulas

>> No.5670926

>>5670922
implying you can't derive them

>> No.5670940

>>5670907
no problem OP.

another way: start from 8-4 sqrt[3] = a^2
have an inspiration
4 - 2sqrt[3] = a^2 / 2

recall (x+y)^2 = x^2 + y^2 +2*x*y
notice that x^2 + y^2 = 4; 2*x*y = -2 sqrt[3]

intuition suggests that x=sqrt[3] and y=-1 makes this work; holy shit, it does

(sqrt[3] -1)^2 = a^2 / 2
2(sqrt[3] - 1)^2 = a^2
sqrt[2]*(sqrt[3]-1) = a

>> No.5670945

>>5670926

OP is looking for a way to simplify some high school algebra. using these formulas is:

1) lighting a furnace to burn a hair
2) focuses on remembering formulas versus doing the derivation

>get on my level

>> No.5670961

>>5670945
it is what i thought would be high school algebra, but actually more complex

>>5670908
answered my question

>>5670892
found my problem

so no need to argue, everyone is right

>> No.5670962

>>5670945
get on your level of what? Highschool kid logic?

>> No.5670971

>>5670962
to give credit where credit is due, your formulas are very general and could be memorized. however, in the context of OP's problem, it's probably a lot better to be familiar with trig manipulations and completing the square than obscure identities. it's just a little overkill is all.

>> No.5671021
File: 1.21 MB, 3000x2000, Spicebush-Swallowtail-Butterfly.jpg [View same] [iqdb] [saucenao] [google]
5671021

>>5670971
I'm not sure that he asked for a way to solve that problem; I pretty much think he asked how to get from that kind of form he got to the one showed in answers. That formula wasnt a overkill. Is the simplest yet more general way of dealing with that kind of radicals. Nuff said.

And about solving that problem of his....yee that cosinus formula lead him to a nasty result; with a little bit of focus and use of geometry he could have solved it way easier without "memorizing" formulas although that cosinus formula is also easily derivable.