document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=776345>Question 776345</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve for x in 10sin^2(x) – 9cos(x) – 12 = 0 \r<BR>\n" );
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document.write( "I've tried pythagorean identities 10 (1-cos^2(x)) – 9cos(x) – 12 = 0 but don't know where to go from there. I know it needs to be in a form that can be used for the zero product rule (no addition or subtraction in the expression), and then from there I need to use the unit circle (which I can do).\r<BR>\n" );
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document.write( "I also tried power reducing/double angle, but that was very confusing for me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #473549 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=473549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 10sin^2(x) - 9cos(x) - 12 = 0<BR>\n" );
document.write( "To get an expression involving only terms in cos(x), we use the identity sin^2(x)+cos^2(x) = 1 -> sin^2(x) = 1 - cos^2(x)<BR>\n" );
document.write( "10(1-cos^2(x)) - 9cos(x) - 12 = 0<BR>\n" );
document.write( "10cos^2(x) + 9cos(x) + 2 = 0<BR>\n" );
document.write( "This can be solved using the quadratic formula, using cos(x) as the variable.<BR>\n" );
document.write( "Alternatively, the expression can actually be factored this way:<BR>\n" );
document.write( "(10cos(x)+5)(cos(x)+2/5) = 0<BR>\n" );
document.write( "This gives 10cos(x) = -5 or cos(x) = -1/2<BR>\n" );
document.write( "and cos(x) = -2/5<BR>\n" );
document.write( "I'll leave it as an exercise to solve for x from here </SPAN>\n" );
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