document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118937>Question 1118937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sin (theta) = 8/17, find the two possible values for [tan(theta) + sec(theta)] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734369 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'll use x for theta.\r<BR>\n" );
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document.write( "the problem then reads:\r<BR>\n" );
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document.write( "sin(x) = 8/17, find the two possible values for (tan(x) + sec(x)\r<BR>\n" );
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document.write( "one way to solve this:\r<BR>\n" );
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document.write( "sin(x) = 8/17 means x = 28.07248694 degrees.\r<BR>\n" );
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document.write( "that's in the first quadrant.\r<BR>\n" );
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document.write( "sin(x) is positive in the first and second quadrants.\r<BR>\n" );
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document.write( "the equivalent angle in the second quadrant is 180 - 28.07248694 = 151.9275132 degrees.\r<BR>\n" );
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document.write( "the two possible values of tan(x) + sec(x) would be:\r<BR>\n" );
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document.write( "1 and 1/3 in the first quadrant and minus 1 and 1/3 in the second quadrant.\r<BR>\n" );
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document.write( "this can be seen in the following graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/062102.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the sine function is .471 in both equations.\r<BR>\n" );
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document.write( "that makes those 2 angles equivalent, because they have the same value for their sine function.\r<BR>\n" );
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document.write( "the tan(x) + sec(x) function is plus 1.667 in the first quadrant and minus 1.667 in the second quadrant.\r<BR>\n" );
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document.write( "i believe this is the way you solve this.\r<BR>\n" );
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document.write( "you find the angle in the four quadrants that have sine = 8/17.\r<BR>\n" );
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document.write( "those two angles were found in the first and second quadrant only.\r<BR>\n" );
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document.write( "you then find tan(x) + sec(x) for those angles.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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