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Trignometry

Hot goIITian

 Joined: 9 Apr 2007 Post: 146
10 Jan 2008 23:58:51 IST
0 People liked this
5
629
find the angle
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

Blazing goIITian

Joined: 3 Dec 2006
Posts: 1043
11 Jan 2008 00:03:29 IST
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Hot goIITian

Joined: 10 Jan 2008
Posts: 107
11 Jan 2008 18:48:02 IST
2 people liked this

Sneha,

sin-1x can be max pi/2 and minimum -pi/2 (as far as i remember the range of  sin-1x)

let  A = sin-1(sin 5)
=> sin A = sin 5 = sin (pi + (5 - pi)) = - sin (5 - pi)
=> sin A = - sin (pi/2 + (5 - 3*pi/2)) = - cos (5 - 3*pi/2)

=> - sin A =
cos (5 - 3*pi/2)

=> cos (pi/2 + A) =
cos (5 - 3*pi/2)

=> pi/2 + A =
5 - 3*pi/2

=>  A =  (5 - 2*pi) is the correct answer.

(remember that answer must lie between -pi/2 and pi/2, and
(5 - 2*pi) does)
.

Cool goIITian

Joined: 7 Dec 2007
Posts: 95
18 Jan 2008 17:17:11 IST
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3pi/4<5<2pi
Range of sininverse(sinx) is ? pi/ to +pi/2
Sin(2pi-5)= -sin5 ---------1
Sininverse(sin(2pi-5)) = 2pi-5 as 2pi-5is in the range
BUT 2pi-5= -sininverse(sin5)
Therefore ans=5-2pi

New kid on the Block

Joined: 19 Jan 2008
Posts: 5
19 Jan 2008 03:50:56 IST
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New kid on the Block

Joined: 4 Jul 2007
Posts: 3
19 Jan 2008 18:55:30 IST
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this is rsa,
range of sin-1 x = -pi/2 to pi/2

sin A = sin 5 = sin (pi + (5 - pi)) = - sin (5 - pi)
sin A = - sin (pi/2 + (5 - 3*pi/2)) = - cos (5 - 3*pi/2)
- sin A = cos (5 - 3*pi/2)
cos (pi/2 + A) = cos (5 - 3*pi/2)
pi/2 + A = 5 - 3*pi/2

A = 5-2pi

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