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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? Tags equation, trigonometric Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Monox D. I-Fly Trigonometry 4 January 29th, 2018 03:56 PM Elecrop Trigonometry 2 April 8th, 2013 02:07 PM naman Trigonometry 1 April 3rd, 2013 05:40 PM sachinrajsharma Trigonometry 7 March 15th, 2013 05:42 PM StevenMx Algebra 8 February 7th, 2009 10:19 AM

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