amruta1997
how to find value of sin 18.......plz explain in detail
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Rezz5
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without the use of the calculator?
amruta1997
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ya
amruta1997
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how 2 derivate it
Rezz5
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taylor expansion can estimate it for you
amruta1997
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i did not get what u want to say
amruta1997
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sauravshakya u may try
amruta1997
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who is taylor
Rezz5
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Taylor Expansion is the way of estimating and function
sinx is \[x-\frac{ x ^{3} }{ 6 }+\frac{ x ^{5} }{ 120 } -...+...\]
sauravshakya
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5*18=90
sin(5*18)=sin90
Let x=18 then,
sin(5x)=sin90
amruta1997
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i think u r wrog somewhere
sauravshakya
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U can proceed from here but this will be too long but it will give u exact value.
amruta1997
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we dont have a formula for sin 5 thete
sauravshakya
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From sin(5x)=1
u need to find the value of sinx
amruta1997
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i mean to say we dont have its expansion
sauravshakya
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sin(5x) = sin(2x + 3x) = sin2x * cos3x + cos2x * sin3x
amruta1997
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hmmmmm
that wd be 22 long
gohangoku58
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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.
amruta1997
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hmmmmmm this wd b an easy one
Rezz5
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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
sauravshakya
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Great!
amruta1997
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but when we will solve the quadrtic equation then we will get two values of sin theta
amruta1997
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which one is great
sauravshakya
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@gohangoku58 's one
amruta1997
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hmmmmmmm
sauravshakya
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because that gives exact value not approximate
amruta1997
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hmmmmm
but two values
amruta1997
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which one to select
amruta1997
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u plz try it once
sauravshakya
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well, sin 18 lies in first quadrant so take positive value
amruta1997
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hmmmmm
amruta1997
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good
gohangoku58
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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...
amruta1997
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i failed 2 use common sence
amruta1997
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no not a cubic but a quadratic u try it
amruta1997
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i tried it jjust now
gohangoku58
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sin 3x= ?
amruta1997
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3sinx-4 sin cube x
gohangoku58
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3sinx-4 sin cube x<----cubic
amruta1997
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no but sin 2 x is also there
gohangoku58
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*cos 2x
amruta1997
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ya
amruta1997
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1-2sin square x
amruta1997
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then we can take sin in common
sauravshakya
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no u cant 1 is there
amruta1997
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r u there on facebook
gohangoku58
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who ?
amruta1997
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sorry for the personal Q
gohangoku58
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we both are there...
amruta1997
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all of u
sauravshakya
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|dw:1353245978780:dw|
amruta1997
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may i know ur id's
amruta1997
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we can contact there also
amruta1997
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saura i will tell u wait
gohangoku58
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what say saura ?
amruta1997
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short form
gohangoku58
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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
amruta1997
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one moment plzz
amruta1997
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2 theta=90-3 theta
amruta1997
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sin 2 theta = cos 3 theta.................sin (90-theta)=costheta