I'm in an online pre-calculus class and my class and online textbook don't explain a thing! My algebra II class from last year was great though! They explained how to do everything! But anyway, we're learning about trigonometry and the lessons these questions are from is titled Solving Trigonometric Equations: Equations that are Factored or are Quadratic. So, if anyone could please explain to me how to do this. And I could probably use the answer as well-especially so I can make sure I'm actually doing it right! But, you don't have to provide the answer if you don't want. At least an explanation on how to do it though.
Solve the equations.
sin x(sin x + 1 ) = 0
tan 3x(tan x -1 ) = 0
cos 2x(2 cos x + 1) = 0
Solve the equations.
sin x(sin x + 1 ) = 0
tan 3x(tan x -1 ) = 0
cos 2x(2 cos x + 1) = 0
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Each of these would be solved the same way. Since the expression on the left is a product of factors, and the right side is zero, then the overall solutions are the union of all solutions for the factors involved.
For example, the first is
sin(x) ( sin(x) + 1 ) = 0, so we must have
sin(x) = 0, which implies x=0, Pi, 2Pi, etc
sin(x) = -1, which implies x=-Pi/2, 3Pi/2, 7Pi/2, etc
So the overall solution is the combined set of above solutions.
For example, the first is
sin(x) ( sin(x) + 1 ) = 0, so we must have
sin(x) = 0, which implies x=0, Pi, 2Pi, etc
sin(x) = -1, which implies x=-Pi/2, 3Pi/2, 7Pi/2, etc
So the overall solution is the combined set of above solutions.