document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118984>Question 1118984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin &#952; = 8/17, find two possible values of (tan &#952; + sec &#952;). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734428 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The drawing below shows the situation for Q1  (ignore the labeling on the x and y axes… the triangles are not to scale).<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28400%2C400%2C+-5%2C+5%2C+-2%2C+10%2C+grid%280%29%2C%0D%0Aline%280%2C0%2C+4%2C0%29%2C%0D%0Aline%284%2C0%2C4%2C8.5%29%2C%0D%0Aline%280%2C0%2C4%2C8.5%29%2C%0D%0Alocate%284.3%2C4.2%2C+%228%22%29%2C%0D%0Alocate%282%2C-0.4%2C+%22x=15%22%29%2C%0D%0Alocate%281.8%2C+5.6%2C+%2217%22%29%2C%0D%0Alocate%280.3%2C0.5%2Ctheta%29%0D%0A%29%0D%0A ALIGN=MIDDLE   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+=+sqrt%2817%5E2+-+8%5E2%29+=+sqrt%28225%29+=+15+ ALIGN=MIDDLE  ALT=\"+x+=+sqrt%2817%5E2+-+8%5E2%29+=+sqrt%28225%29+=+15+\"   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=+tan%28theta%29+=+8%2F15+ ALIGN=MIDDLE  ALT=\"+tan%28theta%29+=+8%2F15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sec%28theta%29+=+1%2Fcos%28theta%29+=+1%2F%2815%2F17%29+=+17%2F15+ ALIGN=MIDDLE  ALT=\"+sec%28theta%29+=+1%2Fcos%28theta%29+=+1%2F%2815%2F17%29+=+17%2F15+\"   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=+tan%28theta%29+%2B+sec%28theta%29+=+8%2F15+%2B+17%2F15+=+25%2F15+=+highlight%28+5%2F3+%29+ ALIGN=MIDDLE  ALT=\"+tan%28theta%29+%2B+sec%28theta%29+=+8%2F15+%2B+17%2F15+=+25%2F15+=+highlight%28+5%2F3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The other angle is in Q2 (where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28pi-x%29+=+sin%28x%29+ ALIGN=MIDDLE  ALT=\"+sin%28pi-x%29+=+sin%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) so the sine value is still 8/17  (i.e. positive) but the tan & sec values are both negative, resulting in   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28-5%2F3%29+ ALIGN=MIDDLE  ALT=\"+highlight%28-5%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   To visualize, flip the triangle across the y-axis where  x<0,  and notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is still measured counter-clockwise from the positive x-axis but now ends in Q2:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28400%2C400%2C+-5%2C+5%2C+-2%2C+10%2C+grid%280%29%2C%0D%0Aline%280%2C0%2C+-4%2C0%29%2C%0D%0Aline%28-4%2C0%2C-4%2C8.5%29%2C%0D%0Aline%280%2C0%2C-4%2C8.5%29%2C%0D%0Alocate%28-4.3%2C4.2%2C+%228%22%29%2C%0D%0Alocate%28-2%2C-0.4%2C+%22x=+-15%22%29%2C%0D%0Alocate%28-1.8%2C+5.4%2C+%2217%22%29%2C%0D%0Alocate%280.3%2C0.5%2Ctheta%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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