Question 928243: Solve the equation sin(theta)+cos(theta)= 2(sin(theta)- cos(theta)), for 0 Found 2 solutions by lwsshak3, KMST:Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Solve the equation sin(theta)+cos(theta)= 2(sin(theta)- cos(theta)), for 0
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sinx+cosx=2sinx-cosx
2cosx-sinx=0
2cosx=sinx
2cosx=√(1-cos^2(x))
4cos^2(x)=1-cos^2(x)
5cos^2(x)-1=0
cos^2(x)=1/5
cosx=±√(1/5)
x≈63.43˚, -116.57˚,-243.43˚, 296.57˚
You can put this solution on YOUR website! To make the equation look simpler, let's define and
Now the equation looks less scary:
and we can solve it for (as a function of , of course): --->--->--->
Now, let's go back to : means --->--->
Since tangent has a period of ,
in the range there are two angles ( apart) that have .
Their approximate measures are and .
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