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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