document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855428>Question 855428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let theta be angle in quadrant II such that sec(theta)=-10/7. Find the exact values of cot(theta) and sin(theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515352 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=515352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> T = Theta.<BR>\n" );
document.write( "sec(T) = -10/7<BR>\n" );
document.write( "this means that the hypotenusse is 10 and the adjacent side of the angle is -7.<BR>\n" );
document.write( "you can find the opposite side of the angle by the pythagorean formula.<BR>\n" );
document.write( "c^2 = a^2 + b^2<BR>\n" );
document.write( "c = 10<BR>\n" );
document.write( "a = -7<BR>\n" );
document.write( "from that formula, solve for b^2 to get:<BR>\n" );
document.write( "b^2 = c^2 - a^2<BR>\n" );
document.write( "substitute for c and a in that formula to get:<BR>\n" );
document.write( "b^2 = (10)^2 - (-7)^2 to get:<BR>\n" );
document.write( "b^2 = 100 - 49 which becomes:<BR>\n" );
document.write( "b^2 = 51 which makes:<BR>\n" );
document.write( "b = sqrt(51)\r<BR>\n" );
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document.write( "you now have:<BR>\n" );
document.write( "angle = T<BR>\n" );
document.write( "hypotenuse = 10<BR>\n" );
document.write( "a = -7<BR>\n" );
document.write( "b = sqrt(51)\r<BR>\n" );
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document.write( "you want to find cot(T):\r<BR>\n" );
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document.write( "cot(T) = adjacent / opposite = -7/sqrt(51)\r<BR>\n" );
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document.write( "you want to find sin(T):\r<BR>\n" );
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document.write( "sin(T) = opposite / hypotenuse = sqrt(51) / 10.\r<BR>\n" );
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document.write( "you can use your calculator to confirm that you did all this correctly.\r<BR>\n" );
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document.write( "my method is as follows:\r<BR>\n" );
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document.write( "assume the angle is in quadrant 1.<BR>\n" );
document.write( "then all of the functions will be positive.<BR>\n" );
document.write( "so solve for the angle as if the angle was in quadrant 1.<BR>\n" );
document.write( "you were given that sec(T) = -10/7<BR>\n" );
document.write( "if T were in quadrant 1, you would get sec(T) = 10/7.<BR>\n" );
document.write( "since sec(T) = 1/cos(T), then solve for:<BR>\n" );
document.write( "1/cos(T) = 10/7<BR>\n" );
document.write( "solving for cos(t) results in:<BR>\n" );
document.write( "cos(T) = 7/10.<BR>\n" );
document.write( "use your calculator to find T to get:<BR>\n" );
document.write( "T = 45.572996<BR>\n" );
document.write( "that's in quadrant 1.<BR>\n" );
document.write( "in quadrant 2, the angle would be (180 - 45.572996) which makes:<BR>\n" );
document.write( "T = 134.427004\r<BR>\n" );
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document.write( "now that you have the angle in quadrant 2, you can check to see if you got the other values correctly.\r<BR>\n" );
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document.write( "sec(134.427004) = -1.428571429<BR>\n" );
document.write( "sin(134.427004) = .7141428429<BR>\n" );
document.write( "cot(134.427004) = -.9801960588\r<BR>\n" );
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document.write( "to confirm that these values are the same as the values you previously calculated, do the following:\r<BR>\n" );
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document.write( "previously you got or were given:<BR>\n" );
document.write( "sec(T) = -10 / 7<BR>\n" );
document.write( "sin(T) = sqrt(51)/10<BR>\n" );
document.write( "cot(T) = -7/sqrt(51)\r<BR>\n" );
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document.write( "put -10/7 in your calculator and you get -1.428571429 which matches sec(134.427004) so that answer is good.\r<BR>\n" );
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document.write( "put sqrt(51)/10 in your calculator and you get .7141428429 which matches sin(134.427004) so that answer is good.\r<BR>\n" );
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document.write( "put -7/sqrt(51) in your calculator and you get -.9801960588 which matches cot(134.427004) so that answer is good.\r<BR>\n" );
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document.write( "everything checks out and your answer is:\r<BR>\n" );
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document.write( "sin(T) = sqrt(51) / 10\r<BR>\n" );
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document.write( "cot(t) = -7 / sqrt(51)\r<BR>\n" );
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document.write( "a picture of your angle is attached.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/mar221.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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