document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=644165>Question 644165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there! How can I answer this question? Please explain to me the solution so I will know how to answer it next time.\r<BR>\n" );
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document.write( "Find cos theta, tan theta and sec theta, if sin theta = -8/17 and 180< theta < 270.\r<BR>\n" );
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document.write( "thank you soooooo much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404859 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=404859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find cos theta, tan theta and sec theta, if sin theta = -8/17 and 180< theta < 270<BR>\n" );
document.write( "**<BR>\n" );
document.write( "use x for theta<BR>\n" );
document.write( "O for opposite side<BR>\n" );
document.write( "A for adjacent side<BR>\n" );
document.write( "H for hypotenuse<BR>\n" );
document.write( "working with reference angle x in quadrant III where sin and cos<0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sinx=-8/17=O/H<BR>\n" );
document.write( "O=-8<BR>\n" );
document.write( "H=17<BR>\n" );
document.write( "By the Pythagorean Theorem<BR>\n" );
document.write( "A=-&#8730;(H^2-O^2)=-&#8730;(17^2-8^2)=-&#8730;(289-64)=-&#8730;225=-15<BR>\n" );
document.write( "cosx=A/H=-15/17 (in quadrant III where cos<0)<BR>\n" );
document.write( "tanx=O/A=-8/-15=8/15 (in quadrant III where tan>0)<BR>\n" );
document.write( "secx=H/A=-17/15 (in quadrant III where sec<0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "An alternate method is to do it algebraically:<BR>\n" );
document.write( "sin^2x+cos^2x=1<BR>\n" );
document.write( "cos^2x=1-sin^2x<BR>\n" );
document.write( "cosx=&#8730;(1-sin^2x)=&#8730;(1-(8/17)^2)=&#8730;(1-64/289)=&#8730;(225/289=15/17<BR>\n" );
document.write( "cosx=-15/17 in quadrant III<BR>\n" );
document.write( "secx=-17/15<BR>\n" );
document.write( "tanx=sinx/cosx=8/15<BR>\n" );
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