document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064092>Question 1064092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8804; x < 360.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+ ALIGN=MIDDLE  ALT=\"+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >csc(x) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+ ALIGN=MIDDLE  ALT=\"+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = csc(x) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9+ ALIGN=MIDDLE  ALT=\"+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+ ALIGN=MIDDLE  ALT=\"+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" >° & <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+150+ ALIGN=MIDDLE  ALT=\"+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "B.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+150+ ALIGN=MIDDLE  ALT=\"+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" >° and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+330+ ALIGN=MIDDLE  ALT=\"+330+\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "C.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60+ ALIGN=MIDDLE  ALT=\"+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" >° & <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120+ ALIGN=MIDDLE  ALT=\"+120+\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "D.) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120+ ALIGN=MIDDLE  ALT=\"+120+\"   DISABLED_style= \"max-width:90%; height:auto;\" >° and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+300+ ALIGN=MIDDLE  ALT=\"+300+\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679128 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=679128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Acsc%28x%29%2B5+=+csc%28x%29%2B9 ALIGN=MIDDLE  ALT=\"3%2Acsc%28x%29%2B5+=+csc%28x%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Acsc%28x%29%2B5-5+=+csc%28x%29%2B9-5 ALIGN=MIDDLE  ALT=\"3%2Acsc%28x%29%2B5-5+=+csc%28x%29%2B9-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 5 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Acsc%28x%29+=+csc%28x%29%2B4 ALIGN=MIDDLE  ALT=\"3%2Acsc%28x%29+=+csc%28x%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Acsc%28x%29-csc%28x%29+=+csc%28x%29%2B4-csc%28x%29 ALIGN=MIDDLE  ALT=\"3%2Acsc%28x%29-csc%28x%29+=+csc%28x%29%2B4-csc%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract csc(x) from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2csc%28x%29+=+4 ALIGN=MIDDLE  ALT=\"2csc%28x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282csc%28x%29%29%2F2+=+4%2F2 ALIGN=MIDDLE  ALT=\"%282csc%28x%29%29%2F2+=+4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28x%29+=+2 ALIGN=MIDDLE  ALT=\"csc%28x%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sin%28x%29%29+=+2%2F1 ALIGN=MIDDLE  ALT=\"1%2F%28sin%28x%29%29+=+2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite csc(x) in terms of sine. Rewrite the \"2\" on the right side as \"2/1\"\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;\" > Apply reciprocals to both sides\r<BR>\n" );
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document.write( "The goal now is to solve <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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Use a <a  rel=nofollow HREF= \"https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png\">unit circle</a> to find points on the unit circle that have a y coordinate of y = 1/2. This happens at theta = 30 and theta = 150 (in Q1 and Q2 respectively)\r<BR>\n" );
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document.write( "So that means x = 30 or x = 150 (where x is the angle in degrees). \r<BR>\n" );
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document.write( "The final answer is <font color=red>Choice A) 30 degrees and 150 degrees</font></font> </SPAN>\n" );
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