document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=928278>Question 928278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation on the interval [0,360) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2Sin%5E2+%28x%29%2B+3Sin%28x%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+2Sin%5E2+%28x%29%2B+3Sin%28x%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a)45(degrees) ,315(degrees)<BR>\n" );
document.write( "b)360(degrees)<BR>\n" );
document.write( "c)60(degrees),300(degrees)<BR>\n" );
document.write( "d)210(degrees),270(degrees),330(degrees) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563553 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=563553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2sin%5E2+%28x%29%2B+3sin%28x%29%2B1=0+ ALIGN=MIDDLE  ALT=\"+2sin%5E2+%28x%29%2B+3sin%28x%29%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2z%5E2%2B+3z%2B1=0+ ALIGN=MIDDLE  ALT=\"+2z%5E2%2B+3z%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+sin%28x%29 ALIGN=MIDDLE  ALT=\"z+=+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+=+sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"z%5E2+=+sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic formula to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2z%5E2%2B+3z%2B1=0+ ALIGN=MIDDLE  ALT=\"+2z%5E2%2B+3z%2B1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You should get these two solutions in terms of z\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+-1%2F2 ALIGN=MIDDLE  ALT=\"+z+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-1 ALIGN=MIDDLE  ALT=\"z+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use each z solution to find the x solutions.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+-1%2F2 ALIGN=MIDDLE  ALT=\"+z+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2+=+sin%28x%29 ALIGN=MIDDLE  ALT=\"-1%2F2+=+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+=+-1%2F2 ALIGN=MIDDLE  ALT=\"sin%28x%29+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+arcsin%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"x+=+arcsin%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+180+-+arcsin%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"x+=+180+-+arcsin%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-30 ALIGN=MIDDLE  ALT=\"x+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+180+-+%28-30%29 ALIGN=MIDDLE  ALT=\"x+=+180+-+%28-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make sure you're in degree mode on your calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-30 ALIGN=MIDDLE  ALT=\"x+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+210 ALIGN=MIDDLE  ALT=\"x+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-30 ALIGN=MIDDLE  ALT=\"x+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > but the original interval for x is [0,360), so add 360 to -30 to get -30+360 = 330\r<BR>\n" );
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document.write( "So the two solutions here are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+330 ALIGN=MIDDLE  ALT=\"x+=+330\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+210 ALIGN=MIDDLE  ALT=\"x+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-1 ALIGN=MIDDLE  ALT=\"z+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29+=+-1 ALIGN=MIDDLE  ALT=\"sin%28x%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+arcsin%28-1%29 ALIGN=MIDDLE  ALT=\"x+=+arcsin%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+270 ALIGN=MIDDLE  ALT=\"x+=+270\"   DISABLED_style= \"max-width:90%; height:auto;\" > Make sure you're in degree mode on your calculator.\r<BR>\n" );
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document.write( "There's only one solution here\r<BR>\n" );
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document.write( "Put together, there are 3 solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+210 ALIGN=MIDDLE  ALT=\"x+=+210\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+270 ALIGN=MIDDLE  ALT=\"x+=+270\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+330 ALIGN=MIDDLE  ALT=\"x+=+330\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you're all done.\r<BR>\n" );
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document.write( "So the final answer is <font color=\"red\">choice D</font>\r<BR>\n" );
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document.write( "If you need more one-on-one help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>. You can ask me a few more questions for free, but afterwards, I would charge you ($2 a problem to have steps shown or $1 a problem for answer only).\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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