document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596365>Question 596365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use appropriate identities to find the exact value of the expression.\r<BR>\n" );
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document.write( "tan120(degrees) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377748 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=377748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you hear or read \"exact value\" in Trig, you should immediately think: \"I'll need special angles for this.\"<br><BR>\n" );
document.write( "To solve problems like this one, you start by expressing the given angle in terms of one ore more special angles. Some possibilities for this one are:<ul><li>tan(2*60)<BR>\n" );
document.write( "For this we could use the tan(2x) formula</li><li>tan(60+60)<BR>\n" );
document.write( "For this we could use the tan(A+B) formula</li><li>tan(90+30)<BR>\n" );
document.write( "For this we could use the tan(A+B) formula. But we would end up with a tan(90) and tan(90) is undefined. So this will not work.</li><li>tan(30+30+60)<BR>\n" );
document.write( "There is no tan(A+B+C) formula so the 4th one is not easy. But, if we want to work that hard, we could use tan(A+B) twice. (I'll show you at the end.)<\li><li>tan(4*30)<BR>\n" );
document.write( "There is no tan(4x) formula. But we could use tan(2x) twice on that one.</li><li>So either of the first two look good. I'll do them both:<BR>\n" );
document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%282x%29+=+%282tan%28x%29%29%2F%281-tan%5E2%28x%29%29 ALIGN=MIDDLE  ALT=\"tan%282x%29+=+%282tan%28x%29%29%2F%281-tan%5E2%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on tan(2(60)), making the \"x\" a 60 we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28120%29+=tan%282%2860%29%29+=+%282tan%2860%29%29%2F%281-tan%5E2%2860%29%29+=+%282sqrt%283%29%29%2F%281-%28sqrt%283%29%29%5E2%29+=+%282sqrt%283%29%29%2F%281-3%29+=+2aqrt%283%29%2F%28-2%29+=+-sqrt%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Using tan(A+B) on tan(60+60), making both A and B 60's we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28120%29+=+tan%2860%2B60%29+=+%28tan%2860%29%2Btan%2860%29%29%2F%281-tan%2860%29%2Atan%2860%29%29+=+%28sqrt%283%29+%2B+sqrt%283%29%29%2F%281-sqrt%283%29%2Asqrt%283%29%29+=+%282sqrt%283%29%29%2F%281-3%29+=+%282sqrt%283%29%29%2F%28-2%29+=+-sqrt%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I'm only going to start the last two so you can see ways to handle I-don't-have-a-formula-for-that situations.<BR>\n" );
document.write( "Using tan(A+B) twice on tan(30+30+60). First I will designate the 30+30 as the \"A\" and 60 as the \"B\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28120%29+=tan%28%2830%2B30%29%2B60%29+=+%28tan%2830%2B30%29+%2B+tan%2860%29%29%2F%281-tan%2830%2B30%29%2Atan%2860%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using tan(A+B) again on tan(30+30), making the A and B both 30's:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28120%29+=tan%28%2830%2B30%29%2B60%29+=+%28tan%2830%2B30%29+%2B+tan%2860%29%29%2F%281-tan%2830%2B30%29%2Atan%2860%29%29+=+%28%28%28tan%2830%29%2Btan%2830%29%29%2F%281-tan%2830%29tan%2830%29%29%29+%2B+tan%2860%29%29%2F%281-%28%28tan%2830%29%2Btan%2830%29%29%2F%281-tan%2830%29tan%2830%29%29%29%2Atan%2860%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you replace tan(60) with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and tan(30) with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > this will work out to the right answer! (Try it if you don't believe me!)<br><BR>\n" );
document.write( "Using tan(2x) twice on tan(4(30)). The first time the \"x\" will be \"2*30\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28120%29+=+tan%284x%29+=+tan%282%282%2A30%29%29%29+=+%282tan%282%2A30%29%2F%281-tan%5E2%282%2A30%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using tan(2x) again on tan(2*30), making the \"x\" a 30:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28120%29+=+tan%284x%29+=+tan%282%282%2A30%29%29+=+%282tan%282%2A30%29%29%2F%281-tan%5E2%282%2A30%29%29+=+%282%28%282tan%2830%29%29%2F%281-tan%5E2%2830%29%29%29%29%2F%281-%28%282tan%2830%29%29%2F%281-tan%5E2%2830%29%29%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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