document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257759>Question 257759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve this problem and the steps w/five key points?<BR>\n" );
document.write( " y = Sin 4x?  I'm a beginner can u help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189653 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189653\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This you really can't solve. You can simplify or graph.<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sin%284x%29 ALIGN=MIDDLE  ALT=\"y+=+sin%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "Now 4x = 2x + 2x, so we get<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sin%282x+%2B+2x%29 ALIGN=MIDDLE  ALT=\"y+=+sin%282x+%2B+2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we have an identity:<BR>\n" );
document.write( "sin(A+B) = sinA cosB + sinB cosA<BR>\n" );
document.write( "or in our case<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%282x%2B2x%29+=+sin2xcos2x+%2B+cos2xsin2x ALIGN=MIDDLE  ALT=\"Sin%282x%2B2x%29+=+sin2xcos2x+%2B+cos2xsin2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But these are the same, so we can write<BR>\n" );
document.write( "(Iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%282x%29 ALIGN=MIDDLE  ALT=\"2sin%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "Now 2x = x + x, so we get<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sin%28x+%2B+x%29 ALIGN=MIDDLE  ALT=\"y+=+sin%28x+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we have an identity:<BR>\n" );
document.write( "sin(A+B) = sinA cosB + sinB cosA<BR>\n" );
document.write( "or in our case<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%28x%2Bx%29+=+sinxcosx+%2B+cosxsinx ALIGN=MIDDLE  ALT=\"Sin%28x%2Bx%29+=+sinxcosx+%2B+cosxsinx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But these are the same, so we can write<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sin%28x%29 ALIGN=MIDDLE  ALT=\"2sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From (iv) and (vii), we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4sin%28x%29 ALIGN=MIDDLE  ALT=\"y+=+4sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );