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May 9th, 2019, 06:22 AM   #1
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Trigonometric equation

Find all the general solutions of the trigonometric equation.
3 sin 2x = -1.
I'm clueless. Please help
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May 9th, 2019, 07:37 AM   #2
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$\displaystyle 3 \sin(2x)=-1$
$\displaystyle \sin(2x)=-\frac{1}{3}$


$\displaystyle 2x=\arcsin(-\frac{1}{3})+2k\pi$
and since we have to reflect we also have:
$\displaystyle 2x=\arcsin(\frac{1}{3})+\pi+2k\pi$


So:
$\displaystyle x=\frac{\arcsin(-\frac{1}{3})+2k\pi}{2}$
or
$\displaystyle x=\frac{\arcsin(\frac{1}{3})+\pi+2k\pi}{2}$

Last edited by Greens; May 9th, 2019 at 07:48 AM. Reason: Fixed Spacing
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May 9th, 2019, 08:27 AM   #3
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Thank you Greens
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May 9th, 2019, 12:02 PM   #4
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Or equivalently, $x = \pi/4 ± \tan^{-1}(√2) + \text{k}\hspace{2px}\pi$.
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May 12th, 2019, 03:13 AM   #5
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Greens can you explain how you come up with the second solution?
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