# Find all solution of the following equation in the interval

• May 5th 2010, 06:45 AM
Nessa214
Find all solution of the following equation in the interval
Find all solution of the following equation in the interval [0,2http://upload.wikimedia.org/math/6/3...fdc6a97e85.png)

2sin^2 x = 2+ cos x
• May 5th 2010, 07:03 AM
mrmohamed
Quote:

Originally Posted by Nessa214
Find all solution of the following equation in the interval [0,2http://upload.wikimedia.org/math/6/3...fdc6a97e85.png)

2sin^2 x = 2+ cos x

HI ALL
Put sin^2x = 1 - cos^2x
2 - 2 cos^2x= 2+ cosx
2 cos^2x + cos x = 0
cos x ( 2 cos x +1 ) =0
cos x = 0 x = pi/2 , x = 3 pi / 2
2 cos x + 1 =0 cos x = -1/2 x = 2 pi/3 , x = 4 pi / 3
S.S = { pi/2 , 3pi/2 , 2 pi/3 , 4 pi/3 }
mrmohamed
• May 5th 2010, 07:35 AM
Nessa214
Quote:

Originally Posted by mrmohamed
HI ALL
Put sin^2x = 1 - cos^2x
2 - 2 cos^2x= 2+ cosx
2 cos^2x + cos x = 0
cos x ( 2 cos x +1 ) =0
cos x = 0 x = pi/2 , x = 3 pi / 2
2 cos x + 1 =0 cos x = -1/2 x = 2 pi/3 , x = 4 pi / 3
S.S = { pi/2 , 3pi/2 , 2 pi/3 , 4 pi/3 }
mrmohamed

thanks so much!