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Trignometry

Hot goIITian

 Joined: 9 Apr 2007 Post: 146
13 Jan 2008 22:23:49 IST
0 People liked this
4
512
find angle
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

1. sin-1sin 10    2 .cos-1cos 10

Blazing goIITian

Joined: 2 Jan 2008
Posts: 504
13 Jan 2008 22:33:08 IST
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1 10
2 10

Blazing goIITian

Joined: 10 Sep 2007
Posts: 1319
13 Jan 2008 22:35:04 IST
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nupz
ur ansewr is wrng i guess
sininverse is outside
so d value inside shud b betwn or in d range of sin inverse n cos inverse
i guess d answer id 10-3pi

do correct if i m wrng

Blazing goIITian

Joined: 5 Nov 2007
Posts: 507
13 Jan 2008 22:46:52 IST
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Even I thought it would be 10 in both cases...
Deedee,could you please tell when it will be so(i mean 10)?

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
13 Jan 2008 22:47:14 IST
2 people liked this

sin 10 = sin (3*pi + (10 - 3*pi)) = - sin (10 - 3*pi) = sin (3*pi - 10)

=> sin-1(sin 10) =  sin-1(sin (3*pi - 10)) = 3*pi - 10 = - (10 - 3*pi)     ANS
lies in [-pi/2, +pi/2] i.e. range of sine inverse

cos 10 = cos (4*pi - (4*pi - 10)) = cos (4*pi - 10)

=> cos-1(cos 10) = cos-1(cos (4*pi - 10)) = 4*pi - 10   ANS
ans lies in [0, pi] i.e. range of cosine inverse

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