document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180791>Question 1180791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question.\r<BR>\n" );
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document.write( "Solve each of the following for 0 <= theta <= 360 degrees <BR>\n" );
document.write( "3sin^2 theta + 2sin theta = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810576 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is 3sin^2(theta) + 2sin(theta) = 0<BR>\n" );
document.write( "factor out sin(theta) to get:<BR>\n" );
document.write( "sin(theta) * (3sin(theta) + 2) = 0<BR>\n" );
document.write( "this is true when sin(theta) = 0 or 3sin(theta) + 2 = 0<BR>\n" );
document.write( "solve for sin(theta) to get:<BR>\n" );
document.write( "sin(theta) = 0 or sin(theta) = -2/3.<BR>\n" );
document.write( "the reference angle (equivalent angle in the first quadrant) will be:<BR>\n" );
document.write( "theta = arcsin(0) = 0 degrees.<BR>\n" );
document.write( "theta = arcsin(2/3) = 41.8103149 degrees.<BR>\n" );
document.write( "note that the trig function is always positive in the first quadrant.<BR>\n" );
document.write( "sin(theta) is 0 when theta = 0 or 180 degrees or 360 degrees.<BR>\n" );
document.write( "sin(theta) is negative in the third and fourth quadrants.<BR>\n" );
document.write( "the reference angle of 41.8103149 in the third and fourth quadrant is found as follows:<BR>\n" );
document.write( "third quadrant = 41.8103149 + 180 = 221.8103149 degrees.<BR>\n" );
document.write( "fourth quadrant = 360 - 41.8103149 = 318.1896851 degrees.<BR>\n" );
document.write( "your angles that satisfy the equation of 3sin^2(theta) + 2sin(theta) = 0 are:<BR>\n" );
document.write( "0,180,360 degrees.<BR>\n" );
document.write( "221.8103149, 318.1896851 degrees.<BR>\n" );
document.write( "a graph of the equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/052201.jpg\"><BR>\n" );
document.write( " </SPAN>\n" );
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