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Grade: 9
        


Find the value of sin 18 degree.



6 years ago

Answers : (2)

Aman Bansal
592 Points
							

Dear Anushka

cos 18° = 4 sin 18° cos 18° (1 - 2sin2 18°)         by the cofunction properties: sin 72° = cos 18°.
            1 = 4 sin 18° (1 - 2sin2 18°)                       Let x = sin 18°, this is known as 
            1 = 4x(1-2x2)                                             substitution, a useful technique in calculus.
8x3-4x+1 = 0                                                         A product is zero only when one of its factors is zero.
8x3-4x+1 = (2x-1)(4x2+2x-1)=0                           (2x-1)=0 implies x= ½=sin 30° > sin 18° ;
                                                                              Since we know sin is increasing on [0°,90°].
            x = (-2 ± [square root of] (4 + 4•4•1))/8                       So we must solve the other factor,
                = (-2 ± [square root of] 20)/8                                     using the quadratic formula.
                = (-2 ± [square root of] 4[square root of] 5)/8
                = (-1 ± [square root of] 5)/4                                       But the sin 18° > 0, so it cannot be negative.
  sin 18°   = ([square root of] (5)-1)/4                                         Hence the middle root is the one we want.

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Aman Bansal

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6 years ago
Aman Bansal
592 Points
							

Dear Anushka 

Dont post the same question again.

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple  to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert

 

 

6 years ago
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