document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=933382>Question 933382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the CAST rule to state the sign of each value. Check using calculator.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) tan 15 degrees<BR>\n" );
document.write( "(b) sin 120 degrees<BR>\n" );
document.write( "(c)cos 135 degrees<BR>\n" );
document.write( "(d) tan(-15 degrees)<BR>\n" );
document.write( "(e) sin(-45 degrees)\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566775 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=566775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here is a pattern:\r<BR>\n" );
document.write( "\n" );
document.write( "In the first quadrant (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I ALIGN=MIDDLE  ALT=\"I\"   DISABLED_style= \"max-width:90%; height:auto;\" >), all ratios are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "    In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=II ALIGN=MIDDLE  ALT=\"II\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28theta%29 ALIGN=MIDDLE  ALT=\"tan+%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are negative.\r<BR>\n" );
document.write( "\n" );
document.write( "    In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=III ALIGN=MIDDLE  ALT=\"III\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan+%28theta%29 ALIGN=MIDDLE  ALT=\"tan+%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive (both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > are negative, so &#8203;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%26%238203%3B%26%238203%3By%26%238203%3B%26%238203%3B ALIGN=MIDDLE  ALT=\"x%26%238203%3B%26%238203%3By%26%238203%3B%26%238203%3B\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28theta%29 ALIGN=MIDDLE  ALT=\"cos+%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are negative.\r<BR>\n" );
document.write( "\n" );
document.write( "    In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=IV ALIGN=MIDDLE  ALT=\"IV\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Of course the reciprocal ratios, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc+%28theta%29 ALIGN=MIDDLE  ALT=\"csc+%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29 ALIGN=MIDDLE  ALT=\"sec%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29 ALIGN=MIDDLE  ALT=\"cot%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > follow the same pattern:\r<BR>\n" );
document.write( "\n" );
document.write( "    In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=II ALIGN=MIDDLE  ALT=\"II\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29 ALIGN=MIDDLE  ALT=\"csc%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29 ALIGN=MIDDLE  ALT=\"sec%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29 ALIGN=MIDDLE  ALT=\"cot%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are negative.\r<BR>\n" );
document.write( "\n" );
document.write( "    In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=III ALIGN=MIDDLE  ALT=\"III\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29 ALIGN=MIDDLE  ALT=\"cot%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29 ALIGN=MIDDLE  ALT=\"csc%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29 ALIGN=MIDDLE  ALT=\"sec%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are negative.\r<BR>\n" );
document.write( "\n" );
document.write( "    In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=IV ALIGN=MIDDLE  ALT=\"IV\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28theta%29 ALIGN=MIDDLE  ALT=\"sec%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=csc%28theta%29 ALIGN=MIDDLE  ALT=\"csc%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cot%28theta%29 ALIGN=MIDDLE  ALT=\"cot%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "then, your answers will be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2815%29 ALIGN=MIDDLE  ALT=\"tan%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees ->In the first quadrant (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I ALIGN=MIDDLE  ALT=\"I\"   DISABLED_style= \"max-width:90%; height:auto;\" >), all ratios are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2815%29=2-sqrt%283%29=0.268 ALIGN=MIDDLE  ALT=\"tan%2815%29=2-sqrt%283%29=0.268\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28120%29 ALIGN=MIDDLE  ALT=\"sin%28120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees ->In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=II ALIGN=MIDDLE  ALT=\"II\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28120%29=sqrt%283%29%2F2=0.866 ALIGN=MIDDLE  ALT=\"sin%28120%29=sqrt%283%29%2F2=0.866\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(c)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28135%29 ALIGN=MIDDLE  ALT=\"cos%28135%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees->In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=II ALIGN=MIDDLE  ALT=\"II\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28theta%29 ALIGN=MIDDLE  ALT=\"+cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28135%29=-1%2Fsqrt%282%29=-0.707 ALIGN=MIDDLE  ALT=\"cos%28135%29=-1%2Fsqrt%282%29=-0.707\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28-15%29 ALIGN=MIDDLE  ALT=\"tan%28-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees -> In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=IV ALIGN=MIDDLE  ALT=\"IV\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28-15%29=sqrt%283%29-2=-0.268 ALIGN=MIDDLE  ALT=\"tan%28-15%29=sqrt%283%29-2=-0.268\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(e) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28-45%29 ALIGN=MIDDLE  ALT=\"sin%28-45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees ->In Quadrant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=IV ALIGN=MIDDLE  ALT=\"IV\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28-45%29=-1%2Fsqrt%282%29=-0.707 ALIGN=MIDDLE  ALT=\"sin%28-45%29=-1%2Fsqrt%282%29=-0.707\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );