Question 965947: 1-Sin x=the square root of 2 cos x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 1-Sin x=the square root of 2 cos x
***
for: (0, 360˚)
1-sinx=√2cosx
square both sides:
1-2sinx+sin^2(x)=2cos^2(x)
1-2sinx+sin^2(x)=2(1-sin^2(x)
1-2sinx+sin^2(x)=2-2sin^2(x)
3sin^2(x)-2sinx-1=0
(3sinx+1)(sinx-1)=0
..
3sinx+1=0
sinx=-1/3
x≈199.47˚, 340.53˚
or
sinx-1=0
sinx=1
x=90˚(reject, extraneous root)
|
|
|
