document.write( "Question 1102370: If cos(t)=-5/6 where pi < t < 3pi/2 , find the values of the following trigonometric functions.
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Algebra.Com's Answer #717070 by ikleyn(52865)\"\" \"About 
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document.write( "You are given that  cos(t) = \"-5%2F6\"  and the angle  \"t\"  is in  QIII.\r\n" );
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document.write( "Then   sin(t) =  \"-sqrt%281-cos%5E2%28t%29%29\" = \"-sqrt%281-%28-5%2F6%29%5E2%29\" = \"-sqrt%28%2836-25%29%2F36%29\" = \"-sqrt%2811%2F36%29\" = \"-sqrt%2811%29%2F6\".\r\n" );
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document.write( "        Notice that I put the sign \"-\" (minus) at sqrt, since the function sine is NEGATIVE in QIII.\r\n" );
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document.write( "The next steps are straightforward.  \r\n" );
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document.write( "a)  cos(2t) = cos^2(t) - sin^2(t) = \"%28-5%2F6%29%5E2+-+%28-sqrt%2811%29%2F6%29%5E2\" = \"25%2F36+-+11%2F36\" = \"14%2F36\" = \"7%2F18\".\r\n" );
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document.write( "b)  sin(2t) = 2*sin(t)*cos(t) = \"2%2A%28-sqrt%2811%29%2F6%29%2A%28-5%2F6%29\" = \"%285%2Asqrt%2811%29%29%2F18\".\r\n" );
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document.write( "c)   cos(t/2) = \"-sqrt%28%281%2Bcos%28t%29%29%2F2%29\" = \"-sqrt%28%281%2B%28-5%2F6%29%29%2F2%29\" = \"-sqrt%28%286-5%29%2F%286%2A2%29%29\" = \"-sqrt%281%2F12%29\" = \"-sqrt%2812%29%2F12\" = \"%28-4%2Asqrt%283%29%29%2F12%29\" = \"-sqrt%283%29%2F3\".\r\n" );
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document.write( "         Again, the sign is \"-\" at sqrt, since cosine is NEGATIVE function in QII, where the angle t/2 is.\r\n" );
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document.write( "d)  sin(t/2) = \"sqrt%28%281-cos%28t%29%29%2F2%29\" = \"sqrt%28%281-%28-5%2F6%29%29%2F2%29\" = \"sqrt%28%286%2B5%29%2F%286%2A2%29%29\" = \"sqrt%2811%2F12%29\" = \"sqrt%28132%29%2F12\" = \"%282%2Asqrt%2833%29%29%2F12%29\" = \"sqrt%2833%29%2F6\".\r\n" );
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document.write( "         The sign is \"+\" at sqrt, since the sine function is POSITIVE in QII, where the angle t/2 is.\r\n" );
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\n" ); document.write( "There are two useful groups of lessons in this site, relevant to this problem.\r
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\n" ); document.write( "\n" ); document.write( "First group is the lesson\r
\n" ); document.write( "\n" ); document.write( "    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS\r
\n" ); document.write( "\n" ); document.write( "and all associated lessons (links) with it.\r
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\n" ); document.write( "\n" ); document.write( "The second group is these lessons\r
\n" ); document.write( "\n" ); document.write( "    - Calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "    - Evaluating trigonometric expressions \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the parts of this online textbook under the topics\r
\n" ); document.write( "\n" ); document.write( "\"Trigonometry. Formulas for trigonometric functions\"   and   \"Trigonometry: Solved problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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