document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283285>Question 283285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question is about functions of standard angles.\r<BR>\n" );
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document.write( "The question is;\r<BR>\n" );
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document.write( "Find sin(-5pi/3)cos(2pi)tan(-13pi/3)cot(-29pi/6)\r<BR>\n" );
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document.write( "I am not sure how to work this out. I have tried breaking down the question to find that sin(-5pi/3) = (sqrt3)/2, cos(2pi) = 0, tan(-13pi/3)= sqrt3 but I can't find what cot(-29pi/6) is equal to.\r<BR>\n" );
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document.write( "In fact, I'm not even sure if the values I obtained for the other three were correct.\r<BR>\n" );
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document.write( "So could you please help me solve this problem.\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Alex </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205700 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=205700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find sin(-5pi/3)cos(2pi)tan(-13pi/3)cot(-29pi/6)\r<BR>\n" );
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document.write( "It looks like all of these revolve around a 30/60/90 triangle.\r<BR>\n" );
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document.write( "sin(30) = 1/2<BR>\n" );
document.write( "cos(30) = sqrt(3)/2<BR>\n" );
document.write( "tan(30) = 1/sqrt(3)<BR>\n" );
document.write( "cot(30) = sqrt(3)<BR>\n" );
document.write( "sin(60) = sqrt(3)/2<BR>\n" );
document.write( "cos(60) = 1/2<BR>\n" );
document.write( "tan(60) = sqrt(3)<BR>\n" );
document.write( "cot(60) = 1/sqrt(3)\r<BR>\n" );
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document.write( "Since it's easier to look at these in degrees, then you can convert radians to degrees by using the following formula:\r<BR>\n" );
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document.write( "degrees = radians * pi * 180 / pi.\r<BR>\n" );
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document.write( "Your original expression is:\r<BR>\n" );
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document.write( "sin(-5pi/3)cos(2pi)tan(-13pi/3)cot(-29pi/6)\r<BR>\n" );
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document.write( "-5pi/3 * 180/pi = -5*180/3 = -300 degrees<BR>\n" );
document.write( "2pi * 180/pi = 360 degrees<BR>\n" );
document.write( "-13pi/3 * 180/pi = -13*180/3 = -780 degrees<BR>\n" );
document.write( "-29pi/6 * 180/pi = -29*180/6 = -870 degrees\r<BR>\n" );
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document.write( "If you add 360 to -300 degrees, you get an equivalent angle of 60 degrees that is in the first quadrant.<BR>\n" );
document.write( "If you subtract 360 from 360 degrees, you get an equivalent angle of 0 degrees that is in the first quadrant.<BR>\n" );
document.write( "If you add 2 * 360 degrees to -780 degrees, you get an equivalent angle off -60 degrees which has a reference angle of 60 degrees that is in the fourth quadrant.<BR>\n" );
document.write( "If you add 3 * 360 to -870 degrees, you get an angle of 210 degrees which has a reference angle of 30 degrees that is in the third quadrant.\r<BR>\n" );
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document.write( "your original expression of:\r<BR>\n" );
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document.write( "sin(-5pi/3)cos(2pi)tan(-13pi/3)cot(-29pi/6) becomes:\r<BR>\n" );
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document.write( "sin(60)cos(0)tan(-60)cot(210)\r<BR>\n" );
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document.write( "sin(60) = sqrt(3)/2)<BR>\n" );
document.write( "cos(0) = 1<BR>\n" );
document.write( "tan(-60) = -tan(60) = -sqrt(3)<BR>\n" );
document.write( "cot(210) = cot(30) = sqrt(3)\r<BR>\n" );
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document.write( "Now all you have to do is multiply them together.\r<BR>\n" );
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document.write( "You can also verify with your calculator.\r<BR>\n" );
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document.write( "Using the calculator in radian mode, I got the following:\r<BR>\n" );
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document.write( "sin(-5pi/3) = .866025404 which is the same as sqrt(3)/2.<BR>\n" );
document.write( "cos(2pi) = 1.<BR>\n" );
document.write( "tan(-13pi/3) = -1.732050808 which is the same as -sqrt(3).<BR>\n" );
document.write( "cot(-29pi/6) = 1.732050808 which is the same as sqrt(3).\r<BR>\n" );
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document.write( "This agrees with the answers I got in degree mode so it's looking good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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