document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122078>Question 122078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #10\r<BR>\n" );
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document.write( "Find the coordinates [r, theta] of all points of intersection:\r<BR>\n" );
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document.write( "r = 2sin(theta)  and  r = 1\r<BR>\n" );
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document.write( "a)       [½, pi/3] and [½, 5pi/3]\r<BR>\n" );
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document.write( "b)       [½, pi/6] and [½, 5pi/6]\r<BR>\n" );
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document.write( "c)       [1, pi/3] and [1, 5pi/3]\r<BR>\n" );
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document.write( "d)       [1, pi/6] and [1, 5pi/6]\r<BR>\n" );
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document.write( "e)       None of these<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 #89607 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=89607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given set of equations \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r=2\sin\left(\theta\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r=1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1=2\sin\left(\theta\right)\"> Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2}=\sin\left(\theta\right)\"> Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE sin^{-1}\left(\frac{1}{2}\right)=\theta\"> Take the arcsine of both sides to isolate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \theta\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \theta=\frac{\pi}{6}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \theta=\frac{5\pi}{6}\"> Take the arcsine of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5pi%2F6 ALIGN=MIDDLE  ALT=\"5pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "So because the answer format is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(r,\theta\right)\"> this means we have the solutions: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,\frac{\pi}{6}\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1,\frac{5\pi}{6}\right)\"> \r<BR>\n" );
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document.write( "So the answer is D)\r<BR>\n" );
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document.write( "Note: Since the second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the first coordinate (which is r) is also 1. So the answers will look like (1,?) and (1,?). So if you had no idea what to do, you could easily eliminate possible answers a) and b) </SPAN>\n" );
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