document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142024>Question 1142024</A>: <I><SPAN STYLE=\"word-break: break-all;\">  if sinx=-3/4 and x is the third quadrant find cos(x/2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762684 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=762684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first find arcsin(3/4)\r<BR>\n" );
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document.write( "it will be equal to 48.59037789 degrees.\r<BR>\n" );
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document.write( "the equivalent angle in the third quadrant is 180 + that = 228.5903779 degrees.\r<BR>\n" );
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document.write( "to confirm, find the sine of that.\r<BR>\n" );
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document.write( "it will be equal to -.75 which is the same as -3/4.\r<BR>\n" );
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document.write( "cos(that angle / 2) = cos(114.29511889) = -.4114378278.\r<BR>\n" );
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document.write( "that should be your answer.\r<BR>\n" );
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document.write( "if you used the half angle formula, you would get:\r<BR>\n" );
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document.write( "cos(x/2) = plus or minus sqrt ( (1 + cos(x) / 2 )\r<BR>\n" );
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document.write( "(1 + cos(x)) / 2 = 1 + cos(228.5903779) / 2 = (1 - .6614378278) / 2 = .1692810861.\r<BR>\n" );
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document.write( "plus or minus sqrt (.1692810861) = .4114378278.\r<BR>\n" );
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document.write( "since cosine is negative in second or third quadrant, then cos(x/2) = -.4114378278.\r<BR>\n" );
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document.write( "the solution was determined in two ways.\r<BR>\n" );
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document.write( "first was by dividing the angle in the third quadrant by two and find the cosine of that.\r<BR>\n" );
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document.write( "second was using the half angle formula.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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