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how to find value of sin 18.......plz explain in detail

Trigonometry
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without the use of the calculator?
ya
how 2 derivate it

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Other answers:

taylor expansion can estimate it for you
i did not get what u want to say
sauravshakya u may try
who is taylor
Taylor Expansion is the way of estimating and function sinx is \[x-\frac{ x ^{3} }{ 6 }+\frac{ x ^{5} }{ 120 } -...+...\]
5*18=90 sin(5*18)=sin90 Let x=18 then, sin(5x)=sin90
i think u r wrog somewhere
U can proceed from here but this will be too long but it will give u exact value.
we dont have a formula for sin 5 thete
From sin(5x)=1 u need to find the value of sinx
i mean to say we dont have its expansion
sin(5x) = sin(2x + 3x) = sin2x * cos3x + cos2x * sin3x
hmmmmm that wd be 22 long
5x= 90 2x+3x=90 3x=90-2x sin 3x= cos 2x now put formula of sin 3x and cos 2x in terms of sin x only.
hmmmmmm this wd b an easy one
18=Pi/10 sin(Pi/10)=0.3090169944 F[x]\[=x-\frac{ x ^{3} }{ 6 }+\frac{ x ^{5} }{ 120 }-... \] f[Pi/10]==0.3090170542 you decide
Great!
but when we will solve the quadrtic equation then we will get two values of sin theta
which one is great
hmmmmmmm
because that gives exact value not approximate
hmmmmm but two values
which one to select
u plz try it once
well, sin 18 lies in first quadrant so take positive value
hmmmmm
good
u'll get a cubic equation, with one root = 0 (can't be, rejected) and 2 other roots.....from which u select one with positive value..... like saura said...
i failed 2 use common sence
no not a cubic but a quadratic u try it
i tried it jjust now
sin 3x= ?
3sinx-4 sin cube x
3sinx-4 sin cube x<----cubic
no but sin 2 x is also there
*cos 2x
ya
1-2sin square x
then we can take sin in common
no u cant 1 is there
r u there on facebook
who ?
sorry for the personal Q
we both are there...
all of u
|dw:1353245978780:dw|
may i know ur id's
we can contact there also
saura i will tell u wait
what say saura ?
short form
4 x^3 - 2 x^2 - 3x + 1 = 0 one root is x=1 which can't be.... i made a typo earlier and wrote that one root is 0
one moment plzz
2 theta=90-3 theta
sin 2 theta = cos 3 theta.................sin (90-theta)=costheta

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