document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175310>Question 1175310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculating trigonometric equations for x in radians.<BR>\n" );
document.write( "Find all the solutions of the equation in the interval [0,2pi).<BR>\n" );
document.write( "Recall that the quadrants in standard positions are numbered counterclockwise, starting in the upper right-hand corner.<BR>\n" );
document.write( "1.5cosx + Square root 3 = 3cosx<BR>\n" );
document.write( "2.3tan²x - 1 = 0<BR>\n" );
document.write( "3.2cos²x - cosx = 1<BR>\n" );
document.write( "4.4sin³x + 2sin²x - 2sinx - 1 = 0<BR>\n" );
document.write( "5.2sinxcosx - sinx = 0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800925 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Treat each equation as an equation in which the variable(s) is/are trig functions.  Solve by regular algebraic methods; then use your unit circle.<br><BR>\n" );
document.write( "I'll just get you started on each one; you won't learn anything from this if I do all the work for you.<br><BR>\n" );
document.write( "1.  5cosx + Square root 3 = 3cosx<BR>\n" );
document.write( "This is a linear equation in cosx.  Solve by getting the variable on one side and the number on the other:<BR>\n" );
document.write( "2cosx = -sqrt(3)<BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "2.  3(tanx)^2 - 1 = 0<BR>\n" );
document.write( "This is a quadratic equation in tanx.  It is also in the form of a difference of squares.  Factor it that way.<BR>\n" );
document.write( "(sqrt(3)tanx+1)(sqrt(3)tanx-1) = 0<BR>\n" );
document.write( "tanx = -1/sqrt(3)  or  tanx = 1/sqrt(3)<BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "3.  2(cosx)^2 - cosx = 1<BR>\n" );
document.write( "This is quadratic in cosx; get everything on one side and factor.<BR>\n" );
document.write( "2(cosx)^2-cosx-1 = 0<BR>\n" );
document.write( "(2cosx+1)(cosx-1) = 0<BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "4.  4(sinx)^3 + 2(sinx)^2 - 2sinx - 1 = 0<BR>\n" );
document.write( "A cubic in sinx; 4 terms, so factor by grouping.<BR>\n" );
document.write( "(2(sinx)^2)(2sinx+1)-(2sinx+1) = 0<BR>\n" );
document.write( "{2(sinx)^2-1)(2sinx+1) = 0<BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "5.2sinxcosx - sinx = 0<BR>\n" );
document.write( "This is quadratic in both sinx and cosx.  Factor out the factor common to both terms.<BR>\n" );
document.write( "(sinx)(2cosx-1) = 0<BR>\n" );
document.write( "...<br><BR>\n" );
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