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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: 1,981 Thanks: 1027 
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: 7,814 Thanks: 1046 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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find, inverse, sin, sqrt, values 
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