How to calculate this product: $$\sin 1^\circ\times\sin 2^\circ\times\cdots\times\sin90^\circ$$
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1Hint: $\sin(90^\circ)=1$, so you can drop that term. For the rest, pair them up as $\sin(x)\sin(90^\circ-x)=\frac12\sin(2x)$. You will also have an extra term $\sin(45^\circ)=2^{-0.5}$. You'll have to repeat this pairing process a few times. – Rushabh Mehta Feb 27 '21 at 17:01
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First, make sure your calculator is in degree mode. – B. Goddard Feb 27 '21 at 17:01
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2The square of your product is the case $n=180$ of Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$. – metamorphy Feb 27 '21 at 17:08
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I get $1.53268\times 10^{-26}$ – Raffaele Feb 27 '21 at 17:22