|

Trignometry

New kid on the Block

 Joined: 18 Jan 2010 Post: 1
18 Jan 2010 19:06:36 IST
5 People liked this
12
12424
how to find the value of sin 18 degree?
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry

how to find the value of sin 18 degree?

Forum Expert
Joined: 19 Oct 2006
Posts: 7804
19 Jan 2010 11:14:56 IST
2 people liked this

## The Derivation of Sin 18°

sin 72° = 2 sin 36° cos 36°                                 by the double angle relationship.
sin 72° = 4 sin 18° cos 18° (1 - 2sin2 18°)         by the double angle relationship, again.
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 ±  (4 + 4•4•1))/8                       So we must solve the other factor,
= (-2 ±  20)/8                                     using the quadratic formula.
= (-2 ±  4 5)/8
= (-1 ±  5)/4                                       But the sin 18° > 0, so it cannot be negative.
sin 18°   = ( (5)-1)/4                                         Hence the middle root is the one we want.

New kid on the Block

Joined: 7 Jan 2010
Posts: 9
31 Jan 2010 14:38:45 IST
3 people liked this

let x=18" then,

5x=90"

2x+3x=90"

2x=90"-3x

sin2x=sin(90"-3x)

sin2x=cos3x                       {since sin (90" - x) =cos x}

2sinxcosx=4cos3x - cos x         {sin 2x= 2sinxcos x...and....cos 3x=4cos3 x-3cosx}

cos x(2sin x - 4 cos2x+3)=0

2 sinx-4 cos 2x +3=0

2 sin x-4(1- sin2x)+3=0

4 sin2x +2 sinx-1=0

hence

sin x=(5)1/2-1/4

sin 18=(5)1/2-1/4

New kid on the Block

Joined: 29 May 2010
Posts: 1
29 May 2010 14:56:05 IST
0 people liked this

The ratio between diagonal and side of any regular pentagon is  , the golden ratio = (1+ Square root of 5) / 2.

In a regular pentagon ABCDE, draw a perpendicular from A on to CD to meet it at F when angle FAD = angle FAC = 18 deg.

Sin 18 = half side / diagonal = 1/2 of [2/(1+ Square root of 5)] = [(Square root of 5)-1]/4

posted by : K SUBBA REDDY 63 years mobile: 9948711151

New kid on the Block

Joined: 16 Nov 2011
Posts: 2
16 Nov 2011 23:13:51 IST
0 people liked this

how to find the value of sin 18 degree?

New kid on the Block

Joined: 16 Nov 2011
Posts: 2
16 Nov 2011 23:19:41 IST
0 people liked this

no post plz on this blog

New kid on the Block

Joined: 26 Feb 2012
Posts: 4
26 Feb 2012 20:59:38 IST
0 people liked this

how to find the value of sin 18 degree?

New kid on the Block

Joined: 17 Mar 2011
Posts: 5
10 Apr 2012 12:41:38 IST
0 people liked this

how do we factorise 8x3 -4x +1 =0

Hot goIITian

Joined: 8 Oct 2011
Posts: 120
17 Apr 2012 00:34:58 IST
0 people liked this

its discriminant is negative

Hot goIITian

Joined: 8 Oct 2011
Posts: 120
17 Apr 2012 00:38:02 IST
0 people liked this

the easiest way to calculate sin 18 approx iscalculate sin15 which is approx equal to sin 18sin(15+3)=sin15 cos3+ cos15 sin3sin3 =0 approxcos3=1 approxso calculate sin15

New kid on the Block

Joined: 12 Jun 2012
Posts: 1
12 Jun 2012 10:28:58 IST
0 people liked this

how to find the value of cos 18 degree?

New kid on the Block

Joined: 31 Jul 2013
Posts: 2
31 Jul 2013 12:23:19 IST
0 people liked this

1

New kid on the Block

Joined: 31 Jul 2013
Posts: 2
31 Jul 2013 12:24:36 IST
0 people liked this

1

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 10085 m Post - 2214
4. edison
 Altitude - 10825 m Post - 7804
5. Sagar Saxena
 Altitude - 8635 m Post - 8064
 Altitude - 6330 m Post - 1958

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone