SOLUTION: Find all values of x in the interval [0, 2π] that satisfy the equation
6 cos(x) + 3 sin(2x) = 0
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-> SOLUTION: Find all values of x in the interval [0, 2π] that satisfy the equation
6 cos(x) + 3 sin(2x) = 0
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Find all values of x in the interval [0, 2π] that satisfy the equation
6 cos(x) + 3 sin(2x) = 0
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6*cos(x) + 3*sin(2x) = 0,
Divide both sides by 3 and replace sin(2x) by 2*sin(x)*cos(x): sin(2x) = 2*sin(x)*cos(x). You will get
2*cos(x) + 2*sin(x)*cos(x) = 0.
Divide both sides by 2. You will get
cos(x) + sin(x)*cos(x) = 0.
Factorize:
cos(x)*(1+sin(x)) = 0.
The equation deploys in two independent equations:
1) cos(x) = 0 ---> x = and/or x = .
2) 1+sin(x) = 0 ---> sin(x) = -1 ---> x = .
Answer. The solutions are and .
