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2sin^2x-2sinx-1=0

Guest Feb 23, 2017
 #1
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+5

2sin^2x-2sinx-1=0

 

\(2sin^2x-2sinx-1=0\)

 

\(sinx=z\)

 

\(2z^2-2z-1=0\) 

 

\(z = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

 

\(z = {2 \pm \sqrt{2^2+4*2*1} \over 2*2}\)

 

\(z = {2 \pm \sqrt{12} \over 4}\)

 

\(z_1=1.3660254 \ Not \ applicable.\ -1 \leq sinx \leq 1\)

 

\(z_2=-0.3660254\)

 

\(sinx=z_2=-0.3660254\)

 

\(x=arcsinx=arcsin-0.3660254\)

 

\(x=-21°28'15''=-0.3747344\ rad\)

 

laugh !

asinus  Feb 23, 2017

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