document.write( "Question 1160136: Use the given information to determine the values of sine 2 theta​, cosine 2 theta, and tangent 2 theta.
\n" ); document.write( "cos theta=8/17; The terminal side of theta lies in quadrant IV. \n" ); document.write( "
Algebra.Com's Answer #783326 by ikleyn(52808)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Use the given information to determine the values of sin(2*theta)​, cos(2*theta), and tan(2*theta).
\n" ); document.write( "cos theta=8/17; The terminal side of theta lies in quadrant IV.
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @MowMow has two deficiencies.\r
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\n" ); document.write( "\n" ); document.write( "        First, it is FATALLY incorrect.\r
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\n" ); document.write( "\n" ); document.write( "        Second, in his post, the educational part of the solution disappeared in full.\r
\n" ); document.write( "\n" ); document.write( "        So, I came to provide a correct solution to this problem in the form as it should be \r
\n" ); document.write( "\n" ); document.write( "        (as it is expected to be).\r
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document.write( "Since  \"cos%28theta%29\" = 8/17  and angle \"theta\" is in quadrant IV,\r\n" );
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document.write( "    \"sin%28theta%29\" = \"-sqrt%281-cos%5E2%28theta%29%29\" = \"-sqrt%281-%288%2F17%29%5E2%29\" = \"-sqrt%28%2817%5E2-8%5E2%29%2F17%5E2%29\" = \r\n" );
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document.write( "                     = \"-sqrt%28%28289-64%29%2F17%5E2%29\" = \"-sqrt%28225%2F17%5E2%29\" = \"-15%2F17\".\r\n" );
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document.write( "Notice that we us sign  '-'  at the square root since angle \"theta\" is in quadrant IV, \r\n" );
document.write( "where 'sin' is negative.\r\n" );
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document.write( "Now  \"sin%282%2Atheta%29\" = \"2%2Asin%28theta%29%2Acos%28theta%29\" = \"2%2A%28-%2815%2F17%29%29%2A%288%2F17%29\" = \"-240%2F289\" = -0.8304.\r\n" );
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document.write( "     (compare this correct approximate value with incorrect value of 0.8304 in the post by @MowMow).\r\n" );
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document.write( "For  \"cos%282%2Atheta%29\",  use the formula\r\n" );
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document.write( "     \"cos%282theta%29\" = \"cos%28theta+%2B+theta%29\" = \"cos%28theta%29%2Acos%28theta%29-sin%28theta%29%2Asin%28theta%29\" = \r\n" );
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document.write( "                       = \"cos%5E2%28theta%29-sin%5E2%28theta%29\" = \"%288%2F17%29%5E2+-+%28-15%2F17%29%5E2\" = \"64%2F289-225%2F289\" =  \"-161%2F289\" = -0.5571.\r\n" );
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document.write( "For \"tan%282%2Atheta%29\",  use\r\n" );
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document.write( "     \"tan%282%2Atheta%29\" = \"sin%282%2Atheta%29%2Fcos%282%2Atheta%29\" = \"%28%28-240%2F289%29%29%2F%28%28-161%2F289%29%29\" = \"240%2F161\" = 1.4907.\r\n" );
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document.write( "     (compare this correct approximate value with incorrect value of -1.4907 in the post by @MowMow).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, and you have clear instructions/guidance on how to do the solution.\r
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\n" ); document.write( "\n" ); document.write( "@MowMow, it is clear from your post, that you \r
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\n" ); document.write( "\n" ); document.write( "     - don't know right-angled triangles\r
\n" ); document.write( "\n" ); document.write( "     - don't know Pythagorean triangles\r
\n" ); document.write( "\n" ); document.write( "     - do not understand the meaning of this assignment\r
\n" ); document.write( "\n" ); document.write( "     - and do'n't know (have no idea) on how to solve it correctly.\r
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\n" ); document.write( "\n" ); document.write( "I observed your contribution to the forum,\r
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\n" ); document.write( "\n" ); document.write( "and with 179% confidence I can say that you have no necessary knowledge to be a Math tutor.\r
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\n" ); document.write( "\n" ); document.write( "I ask you STOP posting to this forum.\r
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