document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202973>Question 1202973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "Can you help me with this one?<BR>\n" );
document.write( "Use the Auxiliary Angle Method to solve 3cos(2x) - 2sin(2x) =1 on 0≤x≤2π, to 3DP.<BR>\n" );
document.write( "I get four solutions, is this correct?<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838200 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=838200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Another approach would be to plot the function <BR>\n" );
document.write( "f(x) = 3cos(2x) - 2sin(2x) - 1<BR>\n" );
document.write( "and look for the x intercepts aka roots.\r<BR>\n" );
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document.write( "I have done so with this Desmos plot<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.desmos.com/calculator/zeflra7phh\">https://www.desmos.com/calculator/zeflra7phh</a><BR>\n" );
document.write( "The blue shaded region represents the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C=+2pi ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C=+2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > aka [0, 2pi]<BR>\n" );
document.write( "2pi = 6.28 approximately\r<BR>\n" );
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document.write( "Each x intercept is labeled on the graph, and also in the left-side panel.<BR>\n" );
document.write( "With Desmos, you can click on the roots to have the coordinates show up.\r<BR>\n" );
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document.write( "The four approximate solutions in that interval are: <BR>\n" );
document.write( "0.351<BR>\n" );
document.write( "2.203<BR>\n" );
document.write( "3.492<BR>\n" );
document.write( "5.344\r<BR>\n" );
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document.write( "To confirm each solution, plug them back one at a time into f(x)<BR>\n" );
document.write( "For instance, let's try x = 0.351<BR>\n" );
document.write( "f(x) = 3cos(2x) - 2sin(2x) - 1<BR>\n" );
document.write( "f(0.351) = 3cos(2*0.351) - 2sin(2*0.351) - 1<BR>\n" );
document.write( "f(0.351) = -0.0008354950597464<BR>\n" );
document.write( "There's some slight rounding error going on. But it's close enough to 0.<BR>\n" );
document.write( "Make sure your calculator is in radian mode.<BR>\n" );
document.write( "I'll let you check the others.<BR>\n" );
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