I added $pi + 0.4478$ which is the lowest positive answer I got from solving the expression and got 3.5894 as the second lowest positive answer. My web assignment marked both 0.4478 and 3.5894 as correct. I added $pi+3.5894$ thinking it would give me my third and final answer, but my web assignment marked it wrong. Is 6.7310 not the third smallest answer? Maybe there is another solution I m failing to find? Troubleshooting help appreciated. Thank you!
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As Michael Medvinsky's answer indicates, you have $0.4478$ and $\pi+0.4478$ (approx), but the third one would be $\pi-0.4478$ (approx), since cosine is an even function (so that $\cos x = \cos -x$). – Brian Tung Nov 04 '15 at 22:16
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Thank you for the clarification. Very helpful! – alsllksjadlkfj_1010 Nov 04 '15 at 22:23
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Also, Michael's answer needs a small edit (see below). – Brian Tung Nov 04 '15 at 22:30
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Possible duplicate of Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $ – alsllksjadlkfj_1010 Feb 27 '17 at 02:57
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The answer is $$\pm\frac{1}{2} \cos ^{-1}\left(\frac{5}{8}\right) +\pi n$$ where $n$ is an integer.
Michael Medvinsky
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1That should be $\pi n$, not $2\pi n$, since the argument of $\cos$ is $2x$, not $x$. – Brian Tung Nov 04 '15 at 22:29