document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919721>Question 919721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if cos theta = 1/3, theta is in Q IV, find the exact value of sin(theta+pie/3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557979 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=557979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if cos theta = 1/3, theta is in Q IV, find the exact value of sin(theta+pie/3)<BR>\n" );
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document.write( "By definition, cos = x/r<BR>\n" );
document.write( "So x = 1 and r = 3<BR>\n" );
document.write( "Then y = -sqrt(3^2-1^2] = -sqrt(8)<BR>\n" );
document.write( "Therefore <BR>\n" );
document.write( "sin(t) = -sqrt(8)/3 = -(2/3)sqrt(2) <BR>\n" );
document.write( "and cos(t) = 1/3<BR>\n" );
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document.write( "Ans:: sin(t + pi/3) = sin(t)cos(pi/3)+cos(t)sin(pi/3)<BR>\n" );
document.write( "= -(2/3)sqrt(2)*(1/2) + (1/3)(sqrt(3)/2)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "= -sqrt(2)/3 + sqrt(3)/6<BR>\n" );
document.write( "----<BR>\n" );
document.write( "= [sqrt(3) - 2sqrt(2)]/6<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "------------------ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );