# SOLVE SIN4X

Those are all the same answer, since 72k is the same as 36(2k), and 360k is the same as 36(10k). (Presumably k in mathbb Z here.) So you got the same answer as the book, just redundantly.

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https://math.stackexchange.com/questions/2975004/how-to-solve-this-trigonometric-equation-sin3x-sin5x-sin6x-sin2x
Hint: use the formula sin x+sin y = 2sin x+yover 2cdot cosx-yover 2 & cos x-cos y = -2sin x+yover 2cdot sinx-yover 2
https://www.quora.com/How-would-I-find-the-number-of-solutions-to-sin-3x-4-sin-x-sin-2x-sin-4x-in-0-lt-x-lt-2-pi
*A2A :- implies sin3x=4sin xsin2xsin4x star Using product to sum formula we get :- implies sin3x=2sin4xleft(cos x-cos3x ight) implies sin3x=2sin4xcos x-2sin4xsin3x ...

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https://math.stackexchange.com/questions/2544864/prove-the-continuity-of-x-sinx-using-epsilon-delta-method
Forget about 2npi and stuff. The essential point is that |sin x-sin y|leq |x-y| for arbitrary x, yinmathbb R. Let an xinmathbb R be given and consider an increment h with |h|leq1 ...

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x^2-cos(x) is increasing and convex on <0,2pi>, hence if you start Newton's iteration at the right of the only root you get a decreasing sequence converging lớn your root (with the chance lớn ...
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left< eginarray l l 2 & 3 \ 5 & 4 endarray ight> left< eginarray l l l 2 & 0 và 3 \ -1 và 1 và 5 endarray ight>

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