document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839173>Question 839173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let S be the set of all solutions to the differential equation y^n = -y.  THe functions y = sinx and y = cosx are solutions and are linearly independent (becasue if asinx+bcosx=0 all x then a=b=0). In fact, one can show that B = {sinx, cosx} is a basis of S.\r<BR>\n" );
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document.write( "(a) Show that y = sin(x+(pi/3)) is an element of S.<BR>\n" );
document.write( "(b) Find the coordinate vector [sin(x+(pi/3)]B    Hint: use a trig sum formula </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505649 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \sin (x + \frac{\pi}{3}) = \sin x \cos \frac{\pi}{3} + \cos x \sin \frac{\pi}{3} = \frac{1}{2} \sin x + \frac{\sqrt{3}}{2} \cos x\">, which is an element of S.\r<BR>\n" );
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document.write( "(b) Just did that in part (a). </SPAN>\n" );
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