document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=973137>Question 973137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the magnitude and direction angle &#952; of the following vectors. Round the magnitude to the nearest tenth, and round the direction angle to the nearest degree, if rounding is necessary.\r<BR>\n" );
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document.write( "v = (-5, -2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595511 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=595511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if this vector starts at the origin, then you will get:\r<BR>\n" );
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document.write( "p1 = (0,0)<BR>\n" );
document.write( "p2 = (-5,-2)\r<BR>\n" );
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document.write( "the x-coordinate of p2 is -5<BR>\n" );
document.write( "the y-coordinate of p2 is -2\r<BR>\n" );
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document.write( "those coordinates form a right triangle with the origin.\r<BR>\n" );
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document.write( "the tangent of the angle of that triangle would be -2/-5.\r<BR>\n" );
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document.write( "tan^-1(2/5) = 21.80140949 degrees.<BR>\n" );
document.write( "that's the reference angle of the triangle in quaedrant 3.<BR>\n" );
document.write( "the angle in quadrant 3 is 180 + 21.80140949 = 201.80140949 degrees.\r<BR>\n" );
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document.write( "that's the direction.\r<BR>\n" );
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document.write( "the magnitude is sqrt((-2)^2 + (-5)^2) = sqrt(4+25) = sqrt(29).\r<BR>\n" );
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document.write( "the direction in quadrant 3 is generally in a south west direction.\r<BR>\n" );
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document.write( "since the reference angle is only 21 degrees, it's closer to west than south.\r<BR>\n" );
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document.write( "halfway south and halfway west would be an angle of 180 + 45 = 225 degrees.\r<BR>\n" );
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