document.write( "Question 674447: Find all solutions of the equation in the interval [0,2pi)\r
\n" ); document.write( "\n" ); document.write( "sin (x+7pi) - sinx - sqrt.2 =0 \n" ); document.write( "

Algebra.Com's Answer #419309 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find all solutions of the equation in the interval [0,2pi)
\n" ); document.write( "sin (x+7pi) - sinx - sqrt.2 =0
\n" ); document.write( "**
\n" ); document.write( "sin addition formula: sin(a+b)=sin a cos b+cos a sin b
\n" ); document.write( "sin(x+7π)=sin x cos 7π+cos x sin 7π)
\n" ); document.write( "cos 7π=-1
\n" ); document.write( "sin 7π=0
\n" ); document.write( "sin x cos 7π+cos x sin 7π)
\n" ); document.write( "sin x*(-1)+cos x*(0)
\n" ); document.write( "sin(x+7π)=-sin x
\n" ); document.write( "..
\n" ); document.write( "sin (x+7π) - sinx - sqrt.2 =0
\n" ); document.write( "-sin x-sin x-√2=0
\n" ); document.write( "-2sin x=√2
\n" ); document.write( "sin x=-√2/2
\n" ); document.write( "x=5π/4 and 7π/4 (in quadrants III and IV where sin<0) \n" ); document.write( "

\n" );