document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170877>Question 1170877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following.\r<BR>\n" );
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document.write( "t=-2pi/3\r<BR>\n" );
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document.write( "(a) Find the reference number t for the value of t.<BR>\n" );
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document.write( "(b) Find the terminal point determined by t.<BR>\n" );
document.write( "(x, y) = \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851068 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You've asked this question before. Here's the solution again:\r<BR>\n" );
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document.write( "**Given:**\r<BR>\n" );
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document.write( "* t = -2π/3\r<BR>\n" );
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document.write( "**(a) Find the reference number t' for the value of t.**\r<BR>\n" );
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document.write( "The reference number t' is the shortest distance along the unit circle from the terminal point determined by t to the x-axis.\r<BR>\n" );
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document.write( "1. **Determine the Quadrant:**<BR>\n" );
document.write( "   * -2π/3 is in the third quadrant.<BR>\n" );
document.write( "   * To see this, note that -π is -3π/3, and -π/2 is -1.5π/3. -2π/3 lies between these values.\r<BR>\n" );
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document.write( "2. **Calculate the Reference Angle:**<BR>\n" );
document.write( "   * Since t is in the third quadrant, the reference angle is calculated as t' = |t - (-π)|.<BR>\n" );
document.write( "   * t' = |-2π/3 - (-π)| = |-2π/3 + π| = |-2π/3 + 3π/3| = |π/3| = π/3\r<BR>\n" );
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document.write( "Therefore, the reference number t' is π/3.\r<BR>\n" );
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document.write( "**(b) Find the terminal point (x, y) determined by t.**\r<BR>\n" );
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document.write( "1. **Use the Reference Angle:**<BR>\n" );
document.write( "   * The reference angle is π/3.<BR>\n" );
document.write( "   * The coordinates for π/3 on the unit circle are (1/2, √3/2).\r<BR>\n" );
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document.write( "2. **Adjust for the Quadrant:**<BR>\n" );
document.write( "   * Since t = -2π/3 is in the third quadrant, both x and y coordinates are negative.<BR>\n" );
document.write( "   * Therefore, the terminal point is (-1/2, -√3/2).\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "(a) t' = π/3<BR>\n" );
document.write( "(b) (x, y) = (-1/2, -√3/2)<BR>\n" );
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