document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870531>Question 870531</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this two part question: Given cos alpha= -4/5, 90 < alpha < 180<BR>\n" );
document.write( "Then find a) sin 2 alpha<BR>\n" );
document.write( "          b) cos 2 alpha </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524914 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=524914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since 90 < alpha < 180 and we're told that cos(alpha) = -4/5, we know sin(alpha) = 3/5. Use a right triangle to see this (it would be a 3,4,5 right triangle). Keep in mind that sin(alpha) is positive because we're in quadrant 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "If 90 < alpha < 180, then doubling each piece gives us 180 < 2alpha < 360\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So 2alpha is in quadrants 3 and 4. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a) Find sin(2alpha)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin(2alpha) = 2*sin(alpha)*cos(alpha)<BR>\n" );
document.write( "sin(2alpha) = 2*(3/5)*(-4/5)<BR>\n" );
document.write( "sin(2alpha) = -24/25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because 180 < 2alpha < 360 and sin(2alpha) = -24/25, this means we're still in quadrants 3 and 4 (where sine is negative). Unfortunately we don't have enough info to determine which quadrant 2alpha is in.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "b) Find cos(2alpha)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cos(2alpha) = cos^2(alpha) - sin^2(alpha)<BR>\n" );
document.write( "cos(2alpha) = (-4/5)^2 - (3/5)^2<BR>\n" );
document.write( "cos(2alpha) = 16/25 - 9/25<BR>\n" );
document.write( "cos(2alpha) = 7/25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because cos(2alpha) is positive and 180 < 2alpha < 360, we now have enough info to conclude that 2alpha is in quadrant 4. This is where cosine is positive. This is assuming we use both pieces of info that sin(2alpha) = -24/25 and cos(2alpha) = 7/25 along with the restriction that 180 < 2alpha < 360 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );