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Trignometry

New kid on the Block

 Joined: 11 Apr 2010 Post: 2
11 Apr 2010 11:58:38 IST
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find value of sin 36 , cos 18?
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry

find value of sin 36 , cos 18?

Cool goIITian

Joined: 26 Mar 2010
Posts: 79
11 Apr 2010 16:14:25 IST
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let 18=A...5A=90....2A+3A=90..2A=90-3A...sin(2A)=sin(90-3A)..sin(2A)=cos(3A)..put values of sin (2A) and cos(3A)get a quadratic and solve it..

Blazing goIITian

Joined: 16 Jan 2010
Posts: 318
16 Apr 2010 19:35:43 IST
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Let A = 180
=> 5A = 900
=> 3A + 2 A = 900
=> 3A = 902 - 2A
=> Sin 3A = Cos 2A
=> 3 Sin A - 4 Sin3 A = 1 - 2 Sin2 A
=> 3 Sin A - 4 Sin3 A - 1 + 2 Sin2 A = 0
=> 4 Sin3A - 2 Sin2 A - 3 Sin A + 1 = 0
putting sin A = x we have,
4 x3 - 2 x2 - 3x + 1 = 0
=> 4x3 - 4 x2 + 2 x2 - 2x - x + 1 = 0
=> 4 x2(x - 1) + 2x (x - 1) - 1 (x - 1) = 0
=> (x - 1) (4x2 + 2x - 1) = 0
either, x = 1 or 4x2 + 2x - 1 = 0
But, since Sin 180 cannot be equal to 1 so,
4x2 + 2x - 1 = 0
Solve this quadratic eqn. and you will get the value of sin 180 i.e., root (5) - 1 / 4
Then find cos x
Then Sin 360 = 2 sin 18<sup>0</sup> . cos 18<sup>0</sup>

New kid on the Block

Joined: 22 Aug 2012
Posts: 2
22 Aug 2012 13:27:05 IST
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find value of sin 36 , cos 18

New kid on the Block

Joined: 22 Aug 2012
Posts: 2
22 Aug 2012 13:30:21 IST
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what is the minimum value of [x] (a) -1 (b) 0 (c) 1 (d)2

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