document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162249>Question 1162249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact values of sin(2θ), cos(2θ), and tan(2θ) when sin θ =-7/12 and 180∘ < 𝜃 < 270∘. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786006 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=786006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's how i think it's going to work.<BR>\n" );
document.write( "you have sin(x) = -7/12<BR>\n" );
document.write( "that makes x = -35.68533471.<BR>\n" );
document.write( "add 360 to that to get the equivalent positive angle of 324.3146653.<BR>\n" );
document.write( "the reference angle for that is 360 - that = 35.68533471.<BR>\n" );
document.write( "the equivalent angle for that in the third quadrant is that plus 180 = 215.6853347.<BR>\n" );
document.write( "take the sine of that and you get -7/12, which is the correct sine for angle x in the third quadrant.<BR>\n" );
document.write( "you should be able to simply find sin(2x), cos(2x), tan(2x), by simply doubling that angle.<BR>\n" );
document.write( "2 times 215.6853347 = 431.3706694.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "x = 215.6853347<BR>\n" );
document.write( "2x = 431.3706694<BR>\n" );
document.write( "sin(2x) = .9476050057<BR>\n" );
document.write( "cos(2x) = .3194444444.....<BR>\n" );
document.write( "tan(2x) = 2.9664567.\r<BR>\n" );
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document.write( "if my assumptions are correct, those are your solutions.\r<BR>\n" );
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document.write( "using trigonometric identities, you shouls get the same answers.\r<BR>\n" );
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document.write( "you are given that sin(x) = -7/12<BR>\n" );
document.write( "that makes x = 215.6853347, as we found out earlier.\r<BR>\n" );
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document.write( "the trigonometric identifies are:\r<BR>\n" );
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document.write( "sin(2x) = 2 * sin(x) * cos(x)<BR>\n" );
document.write( "cos(2x) = cos^2(x) - sin^2(x)<BR>\n" );
document.write( "tan(2x) = 2 * tan(x) / (1 - tan^2(x)\r<BR>\n" );
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document.write( "since we know x, we should be able to find those using the trig identities.\r<BR>\n" );
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document.write( "sin(x) = -.5833333333 stored in variable N<BR>\n" );
document.write( "cos(x) = -,8133248621 stored in variable O<BR>\n" );
document.write( "tan(x) = .7181848465 stored in variable P\r<BR>\n" );
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document.write( "i stored the values in those variables so i don't have to rewrite those values each time i use them.\r<BR>\n" );
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document.write( "the trigonometric identifies are rewritten using those variable names as shown below:\r<BR>\n" );
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document.write( "sin(2x) = 2 * N * O = .9476050057<BR>\n" );
document.write( "cos(2x) = O^2 - N^2 = .3194444444<BR>\n" );
document.write( "tan(2x) = 2 * P / (1 - P^2) = 2.96641567.\r<BR>\n" );
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document.write( "i get the same answers, so both methods seem to work.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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