Question 768400: 16sin^2(x) = 16 − 8cos(x)
I need to find all the solutions to this problem, it says that there are 4 possible solutions.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 16sin^2(x) = 16 − 8cos(x)
I need to find all the solutions to this problem, it says that there are 4 possible solutions.
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for [0,2π]
16sin^2(x) = 16 − 8cos(x)
2sin^2(x)=2-cos(x)
2(1-cos^2(x))=2-cos(x)
2-2cos^2(x)=2-cos(x)
2cos^2(x)+cos(x)=0
cos(x)(2cos(x)+1)=0
..
cos(x)=0
x=π/2 and 3π/2
..
2cos(x)+1=0
cos(x)=-1/2
x=2π/3 and 4π/3
..
solutions: π/2, 3π/2, 2π/3, 4π/3
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