document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=378975>Question 378975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given sin(theta)= -1/5 and tan(theta)< 0, find the exact value of cos(theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #269183 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=269183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If sin(theta) = -1/5 then by the Pythagorean identity,\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F5%29%5E2%29+%2B+cos%5E2%28theta%29+=+1 ALIGN=MIDDLE  ALT=\"%28-1%2F5%29%5E2%29+%2B+cos%5E2%28theta%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+%28theta%29+=+24%2F25 ALIGN=MIDDLE  ALT=\"cos%5E2+%28theta%29+=+24%2F25\"   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%28theta%29+=+%282%2Asqrt%286%29%29%2F5 ALIGN=MIDDLE  ALT=\"cos%28theta%29+=+%282%2Asqrt%286%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (plus or minus)\r<BR>\n" );
document.write( "\n" );
document.write( "However, since tan(theta) < 0 and sin(theta) < 0, it follows that cos (theta) > 0 because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29%2Fcos%28theta%29+=+tan%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29%2Fcos%28theta%29+=+tan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by definition. Therefore we take the positive value of cos(theta), or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282sqrt%286%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282sqrt%286%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );