document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=516252>Question 516252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the point P(t) = (-2, 3):\r<BR>\n" );
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document.write( "a) What is the distance from P to the origin?<BR>\n" );
document.write( "b) What is cos(t)?<BR>\n" );
document.write( "c) What is the x-y coordinate of the point where the line segment from the origin to P intersects <BR>\n" );
document.write( "the unit circle?<BR>\n" );
document.write( "d) What is the x-y coordinate of P(t - &#960;)?<BR>\n" );
document.write( "e) Evaluate tan(t + &#960;)\r<BR>\n" );
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document.write( "So far I think I have:\r<BR>\n" );
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document.write( "a: sqrt(13)<BR>\n" );
document.write( "b: (2)/(sqrt(13)\r<BR>\n" );
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document.write( "Any ideas for the others? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344302 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=344302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You did part a) correctly, but look at the sign on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the given point and then re-think your answer to part b).\r<BR>\n" );
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document.write( "c) Exactly the same as the correct answer to part b).  That is, after all, the whole point of the unit circle -- the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> coordinates ARE the cosine and sine of the angle.\r<BR>\n" );
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document.write( "d) <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\ -\ \pi\">.  Going halfway around the circle from an angle in the 2nd quadrant puts you in the 4th quadrant where the cosine is + and the sine is -.  Your problem doesn't specify whether you want the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> adn <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> coordinates of the point on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{13}\"> radius circle or the unit circle.  On the bigger circle, the numbers will be the same, but the signs opposite:  (2,-3)\r<BR>\n" );
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document.write( "e)  Hint: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \tan\varphi\ =\ \frac{\sin\varphi}{\cos\varphi}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\ +\ \pi\ =\ t\ -\ \pi\">.  You go halfway around the circle -- who cares which direction you go -- right?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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