document.write( "Question 1143417: SinB=-1/2, 3pi/2 < B < 2pi; sinC= 1/4, pi/2 < C < pi find tan(B+C) \n" ); document.write( "
Algebra.Com's Answer #764245 by ikleyn(52852)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            In this post,  my goal is to present the solution in more compact form comparing with the Edwin's post.\r
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document.write( "1.  Since sin(B) = \"-1%2F2\"  and since B is the angle in QIV, where cosine is positive, we have\r\n" );
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document.write( "        cos(B) = \"sqrt%281-sin%5E2%28B%29%29\" = \"sqrt%281-1%2F4%29\" = \"sqrt%283%2F4%29\" = \"sqrt%283%29%2F2\";\r\n" );
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document.write( "        hence,  tan(B) = \"sin%28B%29%2Fcos%28B%29\" = \"%28%28-1%2F2%29%29%2F%28%28sqrt%283%29%2F2%29%29\" = \"-1%2Fsqrt%283%29\".\r\n" );
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document.write( "2.  Since sin(C) = \"1%2F4\"  and since C is the angle in QII, where cosine is negative, we have\r\n" );
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document.write( "        cos(C) = \"-sqrt%281-sin%5E2%28C%29%29\" = \"-sqrt%281-1%2F16%29\" = \"-sqrt%2815%2F16%29\" = \"-sqrt%2815%29%2F4\";\r\n" );
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document.write( "        hence,  tan(C) = \"sin%28C%29%2Fcos%28C%29\" = \"-%28%281%2F4%29%29%2F%28%28sqrt%285%29%2F4%29%29\" = \"-1%2Fsqrt%285%29\".\r\n" );
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document.write( "3.  Now apply the formula for tangent of sum\r\n" );
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document.write( "        tan(B+C) = \"%28tan%28B%29+%2B+tan%28c%29%29%2F%281+-+tan%28B%29%2Atan%28C%29%29\" = .\r\n" );
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document.write( "     At this point, we have the same formula as Edwin has in his post, and further simplifications can be done by the same way as Edwin did. \r\n" );
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\n" ); document.write( "\n" ); document.write( "You can see many other similar problems solved in my 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 part of this online textbook under the topic  \"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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