document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172974>Question 172974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have three questions that I need extreme help on.<BR>\n" );
document.write( "1.  Find sec thata if sin theta=-4/5 and 270 degrees<theta<360 degrees.<BR>\n" );
document.write( "2.  Simplify: (1/sec theta + sin^2 theta/cos theta)cos theta.<BR>\n" );
document.write( "3.  Find the exact value of: cos315 degrees.<BR>\n" );
document.write( "I have to show my work to get any credit.  Please help.<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 #127826 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=127826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note:  I use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead of theta because theta won't render on this system.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29=sqrt%28cos%5E2%28x%29-1%29 ALIGN=MIDDLE  ALT=\"sin%28x%29=sqrt%28cos%5E2%28x%29-1%29\"   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=sqrt%28cos%5E2%28x%29-1%29+=+-4%2F5 ALIGN=MIDDLE  ALT=\"sqrt%28cos%5E2%28x%29-1%29+=+-4%2F5\"   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=cos%5E2%28x%29-1=16%2F25 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29-1=16%2F25\"   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=cos%5E2%28x%29=16%2F25%2B1=41%2F25 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29=16%2F25%2B1=41%2F25\"   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=cos%28x%29=sqrt%2841%29%2F5 ALIGN=MIDDLE  ALT=\"cos%28x%29=sqrt%2841%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29=-sqrt%2841%29%2F5 ALIGN=MIDDLE  ALT=\"cos%28x%29=-sqrt%2841%29%2F5\"   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=sec%28x%29=1%2Fcos%28x%29 ALIGN=MIDDLE  ALT=\"sec%28x%29=1%2Fcos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=5%2Fsqrt%2841%29 ALIGN=MIDDLE  ALT=\"sec%28x%29=5%2Fsqrt%2841%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=-5%2Fsqrt%2841%29 ALIGN=MIDDLE  ALT=\"sec%28x%29=-5%2Fsqrt%2841%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > but you need to rationalize the denominators so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=%285sqrt%2841%29%29%2F41 ALIGN=MIDDLE  ALT=\"sec%28x%29=%285sqrt%2841%29%29%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29=-%285sqrt%2841%29%29%2F41 ALIGN=MIDDLE  ALT=\"sec%28x%29=-%285sqrt%2841%29%29%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "2.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fsec%28x%29+%2B+sin%5E2%28x%29%2Fcos%28x%29%29cos%28x%29 ALIGN=MIDDLE  ALT=\"%281%2Fsec%28x%29+%2B+sin%5E2%28x%29%2Fcos%28x%29%29cos%28x%29\"   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=1%2Fsec%28x%29=cos%28x%29 ALIGN=MIDDLE  ALT=\"1%2Fsec%28x%29=cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%28x%29+%2B+sin%5E2%28x%29%2Fcos%28x%29%29cos%28x%29 ALIGN=MIDDLE  ALT=\"%28cos%28x%29+%2B+sin%5E2%28x%29%2Fcos%28x%29%29cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply LCD of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29\"   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=%28%28cos%5E2%28x%29+%2B+sin%5E2%28x%29%29%2Fcos%28x%29%29cos%28x%29 ALIGN=MIDDLE  ALT=\"%28%28cos%5E2%28x%29+%2B+sin%5E2%28x%29%29%2Fcos%28x%29%29cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28x%29%2Bsin%5E2%28x%29=1 ALIGN=MIDDLE  ALT=\"cos%5E2%28x%29%2Bsin%5E2%28x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fcos%28x%29%29cos%28x%29=1 ALIGN=MIDDLE  ALT=\"%281%2Fcos%28x%29%29cos%28x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. An angle of 315° is equivalent to an angle of -45° either of which is formed by a ray bisecting the right angle formed by the positive x-axis and the negative y-axis.  This ray intersects the unit circle at a point that forms the vertex of an isoceles right triangle, the other two vertices being the origin and the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and having a hypotenuse of length 1.  The Pythagorean theorem gives us that the legs of the triangle are of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The x coordiate of the vertex at the unit circle is positive and the y coordinate is negative because this is a Quadrant IV angle.  Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28315%29=%28sqrt%282%29%2F2%29%2F1=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28315%29=%28sqrt%282%29%2F2%29%2F1=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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