document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73910>Question 73910</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Use the addition and subtraction formulas to simplify  cos(x-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3PI%2F2 ALIGN=MIDDLE  ALT=\"3PI%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "a. cos x<BR>\n" );
document.write( "b. sin x<BR>\n" );
document.write( "c. -cos x<BR>\n" );
document.write( "d. -sin x<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 #52953 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify  cos(x-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3PI%2F2 ALIGN=MIDDLE  ALT=\"3PI%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "The reduction formula that you are looking for is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28alpha+-+beta%29=+cos%28alpha%29%2Acos%28beta%29+%2B+sin%28alpha%29%2Asin%28beta%29 ALIGN=MIDDLE  ALT=\"cos%28alpha+-+beta%29=+cos%28alpha%29%2Acos%28beta%29+%2B+sin%28alpha%29%2Asin%28beta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "For this problem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+=+x ALIGN=MIDDLE  ALT=\"alpha+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta+=+3pi%2F2 ALIGN=MIDDLE  ALT=\"beta+=+3pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "All you now have to do is to make the appropriate substitutions into the formula to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x+-+3pi%2F2%29+=+cos%28x%29%2Acos%283pi%2F2%29+%2B+sin%28x%29%2Asin%283pi%2F2%29 ALIGN=MIDDLE  ALT=\"cos%28x+-+3pi%2F2%29+=+cos%28x%29%2Acos%283pi%2F2%29+%2B+sin%28x%29%2Asin%283pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now recognize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3pi%2F2+=+270 ALIGN=MIDDLE  ALT=\"3pi%2F2+=+270\"   DISABLED_style= \"max-width:90%; height:auto;\" >degrees. Thinking in terms of degrees may make it easier for<BR>\n" );
document.write( "you to visualize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%283pi%2F2%29=cos%28270%29+=+0 ALIGN=MIDDLE  ALT=\"cos%283pi%2F2%29=cos%28270%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%283pi%2F2%29+=+sin%28270%29+=+-1 ALIGN=MIDDLE  ALT=\"sin%283pi%2F2%29+=+sin%28270%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Make these substitutions into the formula and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x+-+3pi%2F2%29+=+cos%28x%29%2A0+%2B+sin%28x%29%2A%28-1%29 ALIGN=MIDDLE  ALT=\"cos%28x+-+3pi%2F2%29+=+cos%28x%29%2A0+%2B+sin%28x%29%2A%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the right side the multiplication by zero makes the first term disappear and the multiplication<BR>\n" );
document.write( "by -1 in the second term makes it become -sin(x). So the answer to this problem is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x-3pi%2F2%29+=+-+sin%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x-3pi%2F2%29+=+-+sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Answer d is the correct selection<BR>\n" );
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document.write( "Hope this problem makes you aware of how the reduction formula for the cosine of the difference<BR>\n" );
document.write( "between two angles works.<BR>\n" );
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