Question 706614: sin(theta) - (root 3)cos(theta) = 1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! sin(theta) - (root 3)cos(theta) = 1
For (0,2π)
sinx-√3cosx=1
sinx-1=√3cosx
square both sides
sin^2x-2sinx+1=3cos^2x=3(1-sin^2x)=3-3sin^2x
4sin^2x-2sinx+2=0
2sin^2x-sinx+1=0
(2sinx+1)(sinx-1)=0
..
2sinx+1=0
sinx=-1/2
x=7π/6, 11π/6 (in quadrants III and IV where sin<0)
or
sinx-1=0
sinx=1
x=π/2
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