document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197232>Question 1197232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If sec x= 3/2 and cosec y= 3; determine cos (x+y)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830419 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sec(x) = 3/2 becomes:<BR>\n" );
document.write( "1/cos(x) = 3/2 which becomes:<BR>\n" );
document.write( "cos(x) = 2/3.<BR>\n" );
document.write( "when cos(x) = 2/3, solve for sin(x) to get sin(x) = sqrt(5)/3<BR>\n" );
document.write( "confirm by cos^2(x) + sin^2(x) = 1 which becomes:<BR>\n" );
document.write( "(2/3)^2 + (sqrt(5)/3)^2 = 1\r<BR>\n" );
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document.write( "you have:<BR>\n" );
document.write( "cos(x) = 2/3<BR>\n" );
document.write( "sin(x) = sqrt(5)/3\r<BR>\n" );
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document.write( "cosec(y) = 3 becomes:<BR>\n" );
document.write( "1/sin(y) = 3 which becomes:<BR>\n" );
document.write( "sin(y) = 1/3<BR>\n" );
document.write( "when sin(y) = 1/3, solve for cos(y) to get cos(y) = sqrt(8)/3<BR>\n" );
document.write( "confirm by cos^2(y) + sin^2(y) = 1 which becomes:<BR>\n" );
document.write( "(sqrt(8)/3)^2 + (1/3)^2 = 1\r<BR>\n" );
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document.write( "you have:<BR>\n" );
document.write( "cos(y) = sqrt(8)/3<BR>\n" );
document.write( "sin(y) = 1/3\r<BR>\n" );
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document.write( "put theme together, you have:<BR>\n" );
document.write( "cos(x) = 2/3<BR>\n" );
document.write( "cos(y) = sqrt(8)/3<BR>\n" );
document.write( "sin(x) = sqrt(5)/3<BR>\n" );
document.write( "sin(y) = 1/3\r<BR>\n" );
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document.write( "cos(x+y) = cos(x)cos(y)-sin(x)sin(y) which becomes<BR>\n" );
document.write( "cos(x+y) = 2/3*sqrt(8)/3 - sqrt(5)/3*1/3 which is equal to .3800873636.\r<BR>\n" );
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document.write( "i also used my calculator to confirm this is true.<BR>\n" );
document.write( "sec(x) = 3/2 becomes 1/cos(x) = 3/2 which becomes cos(x) = 2/3<BR>\n" );
document.write( "cosec(y) = 3 becomes 1/sin(y) = 3 which becomes sin(y) = 1/3<BR>\n" );
document.write( "arccos(2/3) = 48.1896851 degrees.<BR>\n" );
document.write( "arcsin(1/3) = 19.47122063 degrees.<BR>\n" );
document.write( "48.1896851 + 19.47122063 = 67.66090574 degrees.<BR>\n" );
document.write( "cos(67.66090574) = .3800873636.\r<BR>\n" );
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