....I tried using the sum-to-product formulas but am missing a step where I have to convert to different values I guess? Working through entire formula I end up with $\sqrt{3}$. Answer is $-\sqrt{2}/2$. If I convert to exact values using the difference formulas I arrive at the answer but not sure if that's correct.
Evaluating $\sin(\pi/12) - \sin(5\pi/12)$
-1
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trigonometry
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2In your work it's $\sin(-4\pi/24)$ and not $\sin(-8\pi/12)$,also it should be $\sin(6\pi/24)$ and not $\sin(12\pi/12)$ – 2017-02-12
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0That number is clearly negative. I have a suggestion: trust your guts more than your computation skills, always. – 2017-02-12
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0Wow. *FACEPALM* – 2017-02-12
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0Thanks for all the quick responses and letting me know I need a break. – 2017-02-12
1 Answers
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Hint: $\sin(\frac{\pi}{4})$ is the mean of $\sin(\frac{\pi}{12})$ and $\sin(\frac{5\pi}{12})$ and we know $$\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2},$$ and $$\frac{\pi}{12}=\frac{\pi}{4}-\frac{\pi}{6},$$ $$\frac{5\pi}{12}=\frac{\pi}{4}+\frac{\pi}{6}$$