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 May 9th, 2019, 06:22 AM #1 Newbie   Joined: Apr 2019 From: Malawi Posts: 19 Thanks: 0 Math Focus: Trigonometry and calculus Trigonometric equation Find all the general solutions of the trigonometric equation. 3 sin 2x = -1. I'm clueless. Please help
 May 9th, 2019, 07:37 AM #2 Member     Joined: Oct 2018 From: USA Posts: 88 Thanks: 61 Math Focus: Algebraic Geometry $\displaystyle 3 \sin(2x)=-1$ $\displaystyle \sin(2x)=-\frac{1}{3}$ $\displaystyle 2x=\arcsin(-\frac{1}{3})+2k\pi$ 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
 May 9th, 2019, 08:27 AM #3 Newbie   Joined: Apr 2019 From: Malawi Posts: 19 Thanks: 0 Math Focus: Trigonometry and calculus Thank you Greens
 May 9th, 2019, 12:02 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,926 Thanks: 2205 Or equivalently, $x = \pi/4 ± \tan^{-1}(√2) + \text{k}\hspace{2px}\pi$.
 May 12th, 2019, 03:13 AM #5 Newbie   Joined: Apr 2019 From: Malawi Posts: 19 Thanks: 0 Math Focus: Trigonometry and calculus Greens can you explain how you come up with the second solution?

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