document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114151>Question 1114151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The point P(-3,-6) lies on the terminal arm of an angle &#952; in standard position.<BR>\n" );
document.write( "a) Determine the exact values of sin &#952;, cos &#952; and tan &#952;.<BR>\n" );
document.write( "b) Determine the principal angle, &#952;. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729159 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we are given P(-3,-6) on the terminal arm<BR>\n" );
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document.write( "this puts theta in the third quadrant<BR>\n" );
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document.write( "using Pythagorean Theorem with h as the hypotenuse<BR>\n" );
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document.write( "(-3)^2 + (-6)^2 = h^2<BR>\n" );
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document.write( "h^2 = 9 + 36 = 45<BR>\n" );
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document.write( "h = 3 * square root(5)<BR>\n" );
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document.write( "Note in this case theta = 180 + reference angle(alpha), alpha is always measured over the closest distance to the x axis<BR>\n" );
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document.write( "a) sin alpha = -6/3 * square root(5) = -2/square root(5)<BR>\n" );
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document.write( "cos alpha = -3/3 * square root(5) = -1/square root(5)<BR>\n" );
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document.write( "tan alpha = -6/-3 = 2<BR>\n" );
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document.write( "b) tan^(-1) 2 = 63.4349 degrees<BR>\n" );
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document.write( "theta = 180 + 63.4349 = 243.4349 degrees<BR>\n" );
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document.write( "Note -sin alpha = sin theta, -cos alpha = cos theta and tan alpha = tan theta, that is, the sin and cos are negative in the third quadrant and the tan is positive<BR>\n" );
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document.write( "  </SPAN>\n" );
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