document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180314>Question 1180314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact values of the six trigonometric functions of 𝜃 if 𝜃 is in standard position and the terminal side of 𝜃 is in the specified quadrant and satisfies the given condition.<BR>\n" );
document.write( "IV;     on the line 2x + 7y = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810112 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=810112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the line is 2x + 7y = 0<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 2/7 * x.\r<BR>\n" );
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document.write( "this tells you that:\r<BR>\n" );
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document.write( "when the value of x is 0, the value of y is 0.<BR>\n" );
document.write( "when the value of x is 1, the value of y is -2/7.\r<BR>\n" );
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document.write( "from these 2 value, you can draw a triangle.\r<BR>\n" );
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document.write( "the angle at (0,0) is the vertex of the angle.\r<BR>\n" );
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document.write( "the tangent of that angle is opposite / adjacent = (-2/7) / 1 = -2/7.\r<BR>\n" );
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document.write( "the hypotenuse of that triangle is sqrt(-2/7)^2 + 1^2) = sqrt(53/49).\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "adjacent side of angle = 1<BR>\n" );
document.write( "opposite side of angle = -2/7<BR>\n" );
document.write( "hypotenuse = sqrt(53/49).\r<BR>\n" );
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document.write( "let theta represent the angle.\r<BR>\n" );
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document.write( "sin(theta) = opposite / hypotenuse = (-2/7) / sqrt(53/49).<BR>\n" );
document.write( "cos(theta) = adjacent / hypotenuse = 1 / sqrt(53/49).<BR>\n" );
document.write( "tan(theta) = opposite / adjacent = (-2/7) / 1.<BR>\n" );
document.write( "cot(theta) - adjacent / opposite = 1 / (-2/7).<BR>\n" );
document.write( "sec(theta) = hypotenuse / adjacent = sqrt(53/49) / 1.<BR>\n" );
document.write( "csc(theta) = hypotenuse / opposite = sqrt(53/49) / (-2/7).\r<BR>\n" );
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document.write( "note that:\r<BR>\n" );
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document.write( "cot(theta) = 1 / tan(theta)<BR>\n" );
document.write( "sec(theta) = 1 / cos(theta)<BR>\n" );
document.write( "csc(theta) = 1 / sin(theta)'\r<BR>\n" );
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document.write( "sin = sine<BR>\n" );
document.write( "cos = cosine<BR>\n" );
document.write( "tan = tangent<BR>\n" );
document.write( "cot = cotangent<BR>\n" );
document.write( "sec = secant<BR>\n" );
document.write( "csc = cosecant\r<BR>\n" );
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document.write( "to confirm, you can use your calculator.<BR>\n" );
document.write( "arcsin(theta) = (-2/7) / sqrt(53/49) = -15.9453959 degrees.<BR>\n" );
document.write( "that's your angle.<BR>\n" );
document.write( "let x = -15.9453959 degrees.\r<BR>\n" );
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document.write( "sin(x) = -.2747211279<BR>\n" );
document.write( "(-2/7) / sqrt(53/49) = the same.\r<BR>\n" );
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document.write( "cos(x) = .9615239476.<BR>\n" );
document.write( "(1/sqrt(53/49) = the same.\r<BR>\n" );
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document.write( "tan(x) = -.2857142857.<BR>\n" );
document.write( "(-2/7) / 1 = the same.\r<BR>\n" );
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document.write( "cot(x) = 1 / tan(x) = -3.5<BR>\n" );
document.write( "1 / (-2/7) = the same.\r<BR>\n" );
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document.write( "sec(x) = 1 / cos(x) = 1.040015698.<BR>\n" );
document.write( "sqrt(53/49) / 1 the same.\r<BR>\n" );
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document.write( "csc(x) = 1 / sin(x) = -3.640054945.<BR>\n" );
document.write( "sqrt(53/49) / (-2/7) = the same.\r<BR>\n" );
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document.write( "all trig functions point to the same angle.<BR>\n" );
document.write( "that angle is -15.9453959 degrees.\r<BR>\n" );
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document.write( "that's your angle.\r<BR>\n" );
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document.write( "the exact value of the trig functions for that aangle are:\r<BR>\n" );
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document.write( "sin(theta) = opposite / hypotenuse = (-2/7) / sqrt(53/49).<BR>\n" );
document.write( "cos(theta) = adjacent / hypotenuse = 1 / sqrt(53/49).<BR>\n" );
document.write( "tan(theta) = opposite / adjacent = (-2/7) / 1.<BR>\n" );
document.write( "cot(theta) - adjacent / opposite = 1 / (-2/7).<BR>\n" );
document.write( "sec(theta) = hypotenuse / adjacent = sqrt(53/49) / 1.<BR>\n" );
document.write( "csc(theta) = hypotenuse / opposite = sqrt(53/49) / (-2/7).\r<BR>\n" );
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document.write( "since the square root of 53/49 is not a rational number, you have to use it as shown and can't simplify it any further and be exact.\r<BR>\n" );
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document.write( "sqrt(53/49) = sqrt(53) / sqrt(49).\r<BR>\n" );
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document.write( "sqrt(53) is not a rational number.<BR>\n" );
document.write( "sqrt(49) is a rational number.\r<BR>\n" );
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document.write( "sqrt(53/49) is not a rational number because sqrt(53) is not a rational number.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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