document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=627579>Question 627579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the angle sum identities to find the exact value of the trigonometric expression tan 345°\r<BR>\n" );
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document.write( "A.  2 = sqrt3 <BR>\n" );
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document.write( "B.  -2 - sqrt3<BR>\n" );
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document.write( "C.  -2 + sqrt3  <BR>\n" );
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document.write( "D.  2 - sqrt3  \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395000 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=395000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you read or hear \"exact value\" you should learn that it means \"put your calculator down\". These problems can and should be solved by hand. Often the solution will involve special angles whose function values should be well known.<br><BR>\n" );
document.write( "We cannot find tan(345) by hand directly since the reference angle for 345 is 15 and 15 is not a special angle. But by using a sum, difference, double or half angle formula we can find tan(345) if it is<ul><li>a sum of special angles</li><li>a difference of special angles</li><li>twice a special angles</li><li>half a special angles</li></ul>With a little effort you should be able to find a combination that works. There are numerous possibilities:<BR>\n" );
document.write( "345 = 210 + 135 (for which we would use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A%2BB%29=%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29 ALIGN=MIDDLE  ALT=\"tan%28A%2BB%29=%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "345 = 390 - 45 (for which we would use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A-B%29=%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29tan%28B%29%29 ALIGN=MIDDLE  ALT=\"tan%28A-B%29=%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29tan%28B%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "345 = (1/2)690 (for which we would use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28%281%2F2%29x%29+=+%281-cos%28x%29%29%2Fsin%28x%29%7D%7D%29%0D%0Aetc.%0D%0AThese+will+all+work+and+they+will+all+give+us+the+same+answer.+Of+these+three%2C+the+third+oe+is+the+simplest+formula%3A%0D%0Atan%28345%29%0D%0A%7B%7B%7Btan%28%281%2F2%29690%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-cos%28690%29%29%2Fsin%28690%29 ALIGN=MIDDLE  ALT=\"%281-cos%28690%29%29%2Fsin%28690%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28690%29+=+sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"cos%28690%29+=+sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28690%29+=+-1%2F2 ALIGN=MIDDLE  ALT=\"sin%28690%29+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-sqrt%283%29%2F2%29%2F%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"%281-sqrt%283%29%2F2%29%2F%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eliminating the fractions within a fraction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281-sqrt%283%29%2F2%29%2F%28-1%2F2%29%29%2A%282%2F2%29 ALIGN=MIDDLE  ALT=\"%28%281-sqrt%283%29%2F2%29%2F%28-1%2F2%29%29%2A%282%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-sqrt%283%29%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"%282-sqrt%283%29%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+%2B+sqrt%283%29 ALIGN=MIDDLE  ALT=\"-2+%2B+sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You're welcome to try one of the other combinations of special angles that are equal to 345 and see if you get this answer. </SPAN>\n" );
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