multiple angle equations

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November 23rd 2009, 08:35 PM
>_<SHY_GUY>_<

multiple angle equations

$sin2x = \frac{-\sqrt3}{2}$

how to i solve this equation?
November 23rd 2009, 09:53 PM
qmech

First solve...

First solve:

$<br /> <br /> sin y = \frac{-\sqrt3}{2}<br />$

Then solve

$<br /> <br /> y = 2x<br />$
November 23rd 2009, 09:59 PM
bigwave

$sin2x = \frac{-\sqrt{3}}{2}$
$2x = sin^{-1}(\frac{-\sqrt{3}}{2})$
$x= \frac{1}{2}sin^{-1}(\frac{-\sqrt{3}}{2}) = -\frac{\pi}{3}$

check

$sin(2(\frac{-\pi}{3})) = \frac{-\sqrt{3}}{2}$
November 23rd 2009, 09:59 PM
>_<SHY_GUY>_<

Quote:

Originally Posted by qmech

First solve:

$<br /> <br /> sin y = \frac{-\sqrt3}{2}<br />$

Then solve

$<br /> <br /> y = 2x<br />$

hopefully i did it right, but i got $x = \frac{2\pi}{3}$
is there anything else i have to do?
November 23rd 2009, 10:15 PM
bigwave

this is double angle formula...

$sin2X = 2sinXcosX$

to check x plug it back into the original equation....

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