document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158031>Question 1158031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the specified trigonometric ratio for each special angle.\r<BR>\n" );
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document.write( "1. cos(11pi/6)<BR>\n" );
document.write( "2.cot(5pi/4)<BR>\n" );
document.write( "3.sec(4pi/3)<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 #780948 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=780948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 11pi/6 radians * 180 / pi = 11*180/6 = 11*30 = 330 degrees.<BR>\n" );
document.write( "the angle is in the fourth quadrant.<BR>\n" );
document.write( "the reference angle = 360 - 330 = 30 degrees.<BR>\n" );
document.write( "cosine of 30 degrees = sqrt(3)/2<BR>\n" );
document.write( "since the angle is in the fourth quadrant, cosine is positive, therefore the cosine of 330 degrees is sqrt(3)/2.\r<BR>\n" );
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document.write( "5pi/4 radians * 180 / pi = 5 * 180 / 4 = 5 * 45 = 225 degrees.<BR>\n" );
document.write( "the angle is in the third quadrant.<BR>\n" );
document.write( "the reference angle is 225 - 180 = 45 degrees.<BR>\n" );
document.write( "cotangent of 45 degrees = 1 / tangent of 45 degrees = 1<BR>\n" );
document.write( "since the angle is in the third quadrant, cotangent is positive, therefore the cotangent of 225 degrees is 1.\r<BR>\n" );
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document.write( "4pi/3 radians * 180 / pi = 4 * 180 / 3 = 4 * 60 = 240 degrees.<BR>\n" );
document.write( "the angle is in the third quadrant.<BR>\n" );
document.write( "the reference angle is 240 - 180 = 60 degrees.<BR>\n" );
document.write( "secant of 60 degrees = 1 / cosine of 60 degrees = 1 / (1/2) = 2<BR>\n" );
document.write( "since the angle is in the third quadrant, the secant is negative, therefore the secant of 240 degrees = - 2\r<BR>\n" );
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document.write( "to confirm, put your calculator in radian mode and do the following:<BR>\n" );
document.write( "cos(11pi/6)<BR>\n" );
document.write( "1/tan(5pi/4)<BR>\n" );
document.write( "1/cos(4pi/3)\r<BR>\n" );
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document.write( "you will get:<BR>\n" );
document.write( "cos(11pi/6) = .8660254038<BR>\n" );
document.write( "1/tan(5pi/4) = 1<BR>\n" );
document.write( "1/cos(4pi/3) = -2\r<BR>\n" );
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document.write( "enter sqrt(3)/2 in your calculator to find that it is equivalent to  .8660254038 in decimal format.\r<BR>\n" );
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