document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179362>Question 1179362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of the trigonometric function given that sin u = -12/13 and cos v = 24/25. (Both u and v are in Quadrant IV) a)sin (u+v) b)cos(v-u) c)tan(u-v) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808904 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=808904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Find the exact value of the trigonometric function given that \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28u%29+=+-12%2F13 ALIGN=MIDDLE  ALT=\"sin+%28u%29+=+-12%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28v+%29=+24%2F25 ALIGN=MIDDLE  ALT=\"cos+%28v+%29=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using Pythagorean identity to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%29 ALIGN=MIDDLE  ALT=\"cos%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2+%28u%29+%2Bcos%5E2%28u%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2+%28u%29+%2Bcos%5E2%28u%29=1\"   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=%28+-12%2F13%29%5E2+%2Bcos%5E2%28u%29=1 ALIGN=MIDDLE  ALT=\"%28+-12%2F13%29%5E2+%2Bcos%5E2%28u%29=1\"   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%5E2%28u%29=1-%28+-12%2F13%29%5E2 ALIGN=MIDDLE  ALT=\"cos%5E2%28u%29=1-%28+-12%2F13%29%5E2\"   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%5E2%28u%29=1-144%2F169 ALIGN=MIDDLE  ALT=\"cos%5E2%28u%29=1-144%2F169\"   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%5E2%28u%29=25%2F169 ALIGN=MIDDLE  ALT=\"cos%5E2%28u%29=25%2F169\"   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%28u%29=sqrt%2825%2F169%29 ALIGN=MIDDLE  ALT=\"cos%28u%29=sqrt%2825%2F169%29\"   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%28u%29=5%2F13 ALIGN=MIDDLE  ALT=\"cos%28u%29=5%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%29=+-5%2F13+ ALIGN=MIDDLE  ALT=\"cos%28u%29=+-5%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " In the fourth quadrant, the values for cos are positive only, so use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%29=+5%2F13+ ALIGN=MIDDLE  ALT=\"cos%28u%29=+5%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28v%29 ALIGN=MIDDLE  ALT=\"sin%28v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2+%28v%29+%2Bcos%5E2%28v%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2+%28v%29+%2Bcos%5E2%28v%29=1\"   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%5E2+%28v%29+%2B%2824%2F25%29%5E2=1 ALIGN=MIDDLE  ALT=\"sin%5E2+%28v%29+%2B%2824%2F25%29%5E2=1\"   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%5E2+%28v%29+=1-%2824%2F25%29%5E2 ALIGN=MIDDLE  ALT=\"sin%5E2+%28v%29+=1-%2824%2F25%29%5E2\"   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%5E2+%28v%29+=1-576%2F625 ALIGN=MIDDLE  ALT=\"sin%5E2+%28v%29+=1-576%2F625\"   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%5E2+%28v%29+=49%2F625 ALIGN=MIDDLE  ALT=\"sin%5E2+%28v%29+=49%2F625\"   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+%28v%29+=sqrt%2849%2F625%29 ALIGN=MIDDLE  ALT=\"sin+%28v%29+=sqrt%2849%2F625%29\"   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+%28v%29+=7%2F25 ALIGN=MIDDLE  ALT=\"sin+%28v%29+=7%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28v%29+=-7%2F25 ALIGN=MIDDLE  ALT=\"sin+%28v%29+=-7%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " since in Quadrant IV , use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28v%29+=-7%2F25 ALIGN=MIDDLE  ALT=\"sin+%28v%29+=-7%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so we have:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28u%29+=+-12%2F13 ALIGN=MIDDLE  ALT=\"sin+%28u%29+=+-12%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%29=+5%2F13+ ALIGN=MIDDLE  ALT=\"cos%28u%29=+5%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28v%29+=-7%2F25 ALIGN=MIDDLE  ALT=\"sin+%28v%29+=-7%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28v+%29=+24%2F25 ALIGN=MIDDLE  ALT=\"cos+%28v+%29=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " a)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28u%2Bv%29+=sin%28u%29+cos%28v%29+%2B+cos%28u%29+sin%28v%29 ALIGN=MIDDLE  ALT=\"sin+%28u%2Bv%29+=sin%28u%29+cos%28v%29+%2B+cos%28u%29+sin%28v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......substitute given values\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28u%2Bv%29+=%28-12%2F13+%29+%2824%2F25%29+%2B+%285%2F13+%29+%28-7%2F25%29 ALIGN=MIDDLE  ALT=\"sin+%28u%2Bv%29+=%28-12%2F13+%29+%2824%2F25%29+%2B+%285%2F13+%29+%28-7%2F25%29\"   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+%28u%2Bv%29+=-288%2F325++-7%2F65 ALIGN=MIDDLE  ALT=\"sin+%28u%2Bv%29+=-288%2F325++-7%2F65\"   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+%28u%2Bv%29+=-323%2F325 ALIGN=MIDDLE  ALT=\"sin+%28u%2Bv%29+=-323%2F325\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28u%29+=+-12%2F13 ALIGN=MIDDLE  ALT=\"sin+%28u%29+=+-12%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%29=+5%2F13+ ALIGN=MIDDLE  ALT=\"cos%28u%29=+5%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28v%29+=-7%2F25 ALIGN=MIDDLE  ALT=\"sin+%28v%29+=-7%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28v+%29=+24%2F25 ALIGN=MIDDLE  ALT=\"cos+%28v+%29=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28v-u%29+=sin%28u%29+sin%28v%29+%2B+cos%28u%29+cos%28v%29 ALIGN=MIDDLE  ALT=\"cos%28v-u%29+=sin%28u%29+sin%28v%29+%2B+cos%28u%29+cos%28v%29\"   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%28v-u%29+=%28-12%2F13%29+%28-7%2F25%29+%2B+%285%2F13%29+%2824%2F25%29 ALIGN=MIDDLE  ALT=\"cos%28v-u%29+=%28-12%2F13%29+%28-7%2F25%29+%2B+%285%2F13%29+%2824%2F25%29\"   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%28v-u%29+=84%2F325+%2B+24%2F65 ALIGN=MIDDLE  ALT=\"cos%28v-u%29+=84%2F325+%2B+24%2F65\"   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%28v-u%29+=204%2F325 ALIGN=MIDDLE  ALT=\"cos%28v-u%29+=204%2F325\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28u%29+=+-12%2F13 ALIGN=MIDDLE  ALT=\"sin+%28u%29+=+-12%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28u%29=+5%2F13+ ALIGN=MIDDLE  ALT=\"cos%28u%29=+5%2F13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin+%28v%29+=-7%2F25 ALIGN=MIDDLE  ALT=\"sin+%28v%29+=-7%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%28v+%29=+24%2F25 ALIGN=MIDDLE  ALT=\"cos+%28v+%29=+24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28u-v%29=sin%28u-v%29%2Fcos%28u-v%29 ALIGN=MIDDLE  ALT=\"tan%28u-v%29=sin%28u-v%29%2Fcos%28u-v%29\"   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%28u-v%29=%28sin%28u%29+cos%28v%29+-+cos%28u%29+sin%28v%29%29+%2F+%28sin%28u%29+sin%28v%29+%2B+cos%28u%29+cos%28v%29%29 ALIGN=MIDDLE   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%28u-v%29=%28%28-12%2F13%29+%2824%2F25%29+-+%285%2F13%29+%28-7%2F25%29%29+%2F+%28%28-12%2F13%29+%28-7%2F25%29+%2B%285%2F13%29+%2824%2F25%29%29 ALIGN=MIDDLE   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%28u-v%29=%28-253%2F325%29+%2F+%28204%2F325%29 ALIGN=MIDDLE  ALT=\"tan%28u-v%29=%28-253%2F325%29+%2F+%28204%2F325%29\"   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%28u-v%29=-253%2F204 ALIGN=MIDDLE  ALT=\"tan%28u-v%29=-253%2F204\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );