document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032307>Question 1032307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I can't figure this type of trig question; evaluate inverse trig function when the number in the parenthesis is negative.  I can get the answer when it is not negative inside the parenthesis.  Help please!  \r<BR>\n" );
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document.write( "Example:  tan^-1 * (negative of the square root of three divided by three)\r<BR>\n" );
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document.write( "thanks.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646988 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=646988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you make the function positive, then you will always get the angle in the first quadrant.\r<BR>\n" );
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document.write( "once you find the angle in the first quadrant, it's a relatively simple matter to find the quadrant where the function is negative and then find the equivalent angle in that quadrant.\r<BR>\n" );
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document.write( "looking at your example, i see arctan (minus the square root of 3) / 3).\r<BR>\n" );
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document.write( "the tangent function is negative in the second quadrant and the fourth quadrant.\r<BR>\n" );
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document.write( "it is positive in the first quadrant and the third quadrant.\r<BR>\n" );
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document.write( "solve for arctan (square root of 3) / 3.\r<BR>\n" );
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document.write( "your answer will be the angle in the first quadrant.\r<BR>\n" );
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document.write( "arctan (sqrt(3)/3 = 30 degrees.\r<BR>\n" );
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document.write( "the tangent is negative in the second quadrant and the fourth quadrant.\r<BR>\n" );
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document.write( "converting an angle from the first quadrant to any quadrant is given by the formulas.\r<BR>\n" );
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document.write( "second quadrant angle = 180 - first quadrant angle.<BR>\n" );
document.write( "third quadrant angle = 180 + first quadrant angle.<BR>\n" );
document.write( "fourth quadrant angle = 360 - first quadrant angle.\r<BR>\n" );
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document.write( "since your tangent function is negative, then you are looking for the equivalent angle in the second quadrant and the fourth quadrant.\r<BR>\n" );
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document.write( "your angle will be 180 - 30 = 150 in the second quadrant and it will be 360 - 30 = 330 in the fourth quadrant.\r<BR>\n" );
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document.write( "you can confirm using your calculator.\r<BR>\n" );
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document.write( "find tan(150) and you get -.5773502692.\r<BR>\n" );
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document.write( "find tan(330) and you get -.5773502692 as well.\r<BR>\n" );
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document.write( "use your calculator to find -sqrt(3)/3 and it will say that it is equal to -.5773502692.\r<BR>\n" );
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document.write( "this confirms the answer is -sqrt(3)/3.\r<BR>\n" );
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document.write( "your angles are either 150 degrees or 330 degrees.\r<BR>\n" );
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document.write( "both give you the tan function of -sqrt(3)/3 which is equal to -.5773502692.\r<BR>\n" );
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document.write( "in the first quadrant all the functions are positive.<BR>\n" );
document.write( "in the second quadrant, sine is positive, cosine is negative, tangent is sine/cosine which is negative.<BR>\n" );
document.write( "in the third quadrant, sine is negative, cosine is negative, tangent is sine/cosine which is positive.<BR>\n" );
document.write( "in the fourth quadrant, sine is negative, cosine is positive, tangent is sine/cosine which is negative.\r<BR>\n" );
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document.write( "it's all based on the unit circle.<BR>\n" );
document.write( "sine = y/hypotenuse<BR>\n" );
document.write( "cosine = x/hypotenuse<BR>\n" );
document.write( "tangent = y/x\r<BR>\n" );
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document.write( "in the first quadrant, y is positive and x is positive.<BR>\n" );
document.write( "in the second quadrant, y is positive and x is negative.<BR>\n" );
document.write( "in the third quadrant, y is negative and x is negative.<BR>\n" );
document.write( "in the fourth quadrant y is negative and x is positive.\r<BR>\n" );
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document.write( "the hypotenuse is always positive.\r<BR>\n" );
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document.write( "if you graph y = tan(x), you can see the same solutions as well.\r<BR>\n" );
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document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/043002.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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