document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093700>Question 1093700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact value of tan (2 &#952;)<BR>\n" );
document.write( "cos (&#952;) = - (15)/(17) and &#952; terminates in QII\r<BR>\n" );
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document.write( "Select one:<BR>\n" );
document.write( "a. 161/289<BR>\n" );
document.write( "b. 120/289<BR>\n" );
document.write( "c. - (240)/(161)<BR>\n" );
document.write( "d. - (240)/(289) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #708538 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=708538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> T stands for theta.\r<BR>\n" );
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document.write( "you have cos(T) = -12/17 and T terminates in the second quadrant.\r<BR>\n" );
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document.write( "17 is the hypotenuse of the right triangle formed and 15 is one leg of the right triangle formed.\r<BR>\n" );
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document.write( "the other leg of the right triangle formed is equal to sqrt(17^2 - 15^2) = 8. \r<BR>\n" );
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document.write( "this is found through use of the pythagorean formula.\r<BR>\n" );
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document.write( "the legs of the right triangle formed in the second quadrant have a value of x = -15, y = 8 and hypotenuse = 17.\r<BR>\n" );
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document.write( "you have tan(T) = 8/-15 which is equivalent to -8/15.\r<BR>\n" );
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document.write( "the formula for tan(2T) is tan(2T) = 2 * tan(T) / (1 - tan^2(T)\r<BR>\n" );
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document.write( "tan(T) = -8/15.\r<BR>\n" );
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document.write( "tan^2(T) = (-8/15)^2 = 64/225.\r<BR>\n" );
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document.write( "2 * tan(T) = -16/15.\r<BR>\n" );
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document.write( "1 - tan^2(T) = 161/225.\r<BR>\n" );
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document.write( "formula becomes tan(2T) = (-16/15) / (161/225) which becomes tan(2T) = -16/15 * 225/161 which becomes tan(2T) = (-16*225) / (15/161) which then becomes tan(2T)<BR>\n" );
document.write( " = (-16*15) / 161 which finally becomes tan(2T) = -240/161.\r<BR>\n" );
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document.write( "that's selection c.\r<BR>\n" );
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document.write( "the angle T is equal to arccos(-15/17) = 151.9275131 degrees.\r<BR>\n" );
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document.write( "that's in the second quadrant.\r<BR>\n" );
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document.write( "the angle (2T) is equal to 2 times that = 303.8550261.\r<BR>\n" );
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document.write( "that's in the fourth quadrant.\r<BR>\n" );
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document.write( "tan(T) = tan(151.9275131) = -.53333333333 which is the same as -8/15.\r<BR>\n" );
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document.write( "tan(2T) = tan(303.8550261) = -1.49068323 which is the same as -240/161.\r<BR>\n" );
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document.write( "cos(T) = cos(151.9275131) = -.8823529412 which is the same as -15/17.\r<BR>\n" );
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document.write( "everything checks out so the solution is looking good.\r<BR>\n" );
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document.write( "selection c is your answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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