document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158076>Question 1158076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each angle is described by one of its trigonometric ratios and the quadrant in<BR>\n" );
document.write( "which its terminal side is located. Find the requested trigonometric ratio for the angle.\r<BR>\n" );
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document.write( "8. Find tan θ given sinθ = 1/2 with a terminal side in Quadrant II.<BR>\n" );
document.write( "9. Find cot θ given cosθ = −4/5 with a terminal side in Quadrant III.<BR>\n" );
document.write( "10. Find csc θ given tanθ = −2/9 with a terminal side in Quadrant IV. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781026 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \tan\theta\"> given <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sin\theta\ =\ \frac{1}{2}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \theta\ \in\ QII\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\theta\ =\ \frac{1}{2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2\theta\ =\ \frac{1}{4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\theta\ =\ 1\ -\ \sin^2\theta\ =\ \frac{3}{4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\theta\ =\ \pm\frac{sqrt{3}}{2}\">\r<BR>\n" );
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document.write( "But cosine in QII is negative so reject the positive value.\r<BR>\n" );
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document.write( "Recall that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\varphi\ =\ \frac{\sin\varphi}{\cos\varphi}\">\r<BR>\n" );
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document.write( "Hence,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \tan\theta\ =\ \frac{\frac{1}{2}}{\frac{-\sqrt{3}}{2}}\ =\ -\frac{1}{\sqrt{3}}\ =\ -\frac{\sqrt{3}}{3}\"><BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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