My Math Forum find the values of sin inverse sqrt 5

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 December 22nd, 2016, 02:53 PM #1 Newbie   Joined: Dec 2016 From: egypt Posts: 3 Thanks: 0 find the values of sin inverse sqrt 5 Find the values of sin inverse sqrt 5 I'm stuck with this one; please someone help me. Last edited by skipjack; December 24th, 2016 at 05:34 AM.
 December 22nd, 2016, 03:21 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,427 Thanks: 1314 what is the range of the sine function? what is the approximate value of $\sqrt{5}$ ? do you see a problem here? unless you mean $\sin\left(\dfrac{1}{\sqrt{5}}\right)$ is that what you mean?
 December 22nd, 2016, 05:52 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,934 Thanks: 1128 Math Focus: Elementary mathematics and beyond $\displaystyle y=\sin^{-1}(\sqrt5)$ $\displaystyle \sin(y)=\sqrt5$ $\displaystyle e^{iy}-e^{-iy}=2i\sqrt5$ $\displaystyle \frac{e^{2iy}-1}{e^{iy}}=2i\sqrt5\Rightarrow e^{2iy}-2i\sqrt5e^{iy}-1=0\implies y=\log(i(\sqrt5\pm2))/i$ $\displaystyle \sin^{-1}(\sqrt5)=\log(i(\sqrt5\pm2))/i+2k\pi,k\in\mathbf{Z}$
 December 23rd, 2016, 10:18 AM #4 Newbie   Joined: Dec 2016 From: egypt Posts: 3 Thanks: 0 ty so much

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