Question 444050: solve sin(θ)-√(3)cos(θ)=√(3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! solve sin(θ)-√(3)cos(θ)=√(3)
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use x for theta
assume 0< x< 360 deg or 0< x< 2π radians
sinx-√3cosx=√3
sinx=√3+√3cosx=√3(1+cosx)
square both sides
sin^2x=3(1+2cosx+cos^2x)
1-cos^2x=3+6cosx+3cos^2x
4cos^2x+6cosx+2=0
2cos^2x+3cosx+1=0
(2cosx+1)(cosx+1)=0
2cosx+1=0
cosx=-1/2
x=120 and 240 deg or 2π/3 and 4π/3 radians
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cosx+1=0
cosx=-1
x=180 deg or π radians
ans:
x=120, 240, and 180 deg or 2π/3, 4π/3 and π radians
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