document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=880271>Question 880271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin^4(theta)=cos^5(theta),then what is the value of 'theta' ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #531356 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=531356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm not sure there is an analytical solution. I spent a few minutes trying to derive one but gave up and solved it by iteration. That is, select an initial value of theta and iterively converge to a more precise value.<BR>\n" );
document.write( "Using x instead of theta, the given expression is<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E4%28x%29+=+cos%5E5%28x%29%29 ALIGN=MIDDLE  ALT=\"sin%5E4%28x%29+=+cos%5E5%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or by dividing each side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E4%28x%29 ALIGN=MIDDLE  ALT=\"cos%5E4%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "(2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%5E4%28x%29+=+cos%28x%29 ALIGN=MIDDLE  ALT=\"tan%5E4%28x%29+=+cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the absolute value of the cosine function is less than or equal to one, and the tan(45) is one, start x at 45 degrees and get<BR>\n" );
document.write( "(3) at x = 45, LS = 1, RS = .335, note that LS is greater than the RS   <BR>\n" );
document.write( "Now decrease x, <BR>\n" );
document.write( "(4) at x = 40, LS = .4957, RS = .766, note LS is now less than RS, we went too far, so x lies between 40 and 45.  <BR>\n" );
document.write( "(5) at x = 43, LS = .756, RS = .731, LS is greater than RS, now x is between 40 and 43.      <BR>\n" );
document.write( "(6) at x = 42.5 LS = .7050, RS = .7372 LS is less than RS, went too far, now x is between  42.5 and 43.    <BR>\n" );
document.write( "Keep doing this until you get to  <BR>\n" );
document.write( "(7) x = 42.78634   <BR>\n" );
document.write( "To check this use (1) <BR>\n" );
document.write( "Is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E4%2842.78634%29+=+cos%5E5%2842.78634%29%29 ALIGN=MIDDLE  ALT=\"sin%5E4%2842.78634%29+=+cos%5E5%2842.78634%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)?  <BR>\n" );
document.write( "Is (0.212892 = 0.212892)? Yes<BR>\n" );
document.write( "Answer; theta equals approximately 42.78634 degrees.\r<BR>\n" );
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