document.write( "Question 1144070: Use De moivres theorem to obtain the identity for the following
\n" ); document.write( "A. Sin(7θ)
\n" ); document.write( "B. Cos(6θ) \n" ); document.write( "
Algebra.Com's Answer #765092 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Using DeMoivre's theorem:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Using the binomial theorem:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we use\r\n" );
document.write( "\r\n" );
document.write( "i2 = -1\r\n" );
document.write( "i3 = -i\r\n" );
document.write( "i4 = 1\r\n" );
document.write( "i5 = i\r\n" );
document.write( "i6 = -1\r\n" );
document.write( "i7 = -i\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We can equate the two expressions for cos(7q) + i∙sin(7q)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We equate the REAL parts on each side:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We equate the IMAGINARY parts on both sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Dividing through by i:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have identities for both cos(7q) and sin(7q)\r\n" );
document.write( "\r\n" );
document.write( "You do the other one the same way.  I'll help you with the binomial theorem part:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );