document.write( "Question 180062: Find sin B and cot B if cosB=-1/4 and tan B>0. \n" ); document.write( "
Algebra.Com's Answer #854680 by ikleyn(53937)\"\" \"About 
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\n" ); document.write( "Find sin(B) and cot(B) if cos(B) = -1/4 and tan(B) > 0.
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\n" ); document.write( "\n" ); document.write( "        Calculations in the post by @HyperBrain are incorrect.\r
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\n" ); document.write( "\n" ); document.write( "        For correct solution, see my post below.\r
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document.write( "Since cos(B) is negative and tan(B) is positive (given), we conclude from it that \r\n" );
document.write( "angle B is in QIII.\r\n" );
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document.write( "In QIII sine is negative, so we write\r\n" );
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document.write( "    sin(B) = \"-sqrt%281-cos%5E2%28B%29%29\" = \"-sqrt%281-%28-1%2F4%29%5E2%29\" = \"-sqrt%281-1%2F16%29\" = \"-sqrt%2815%29%2F4\".\r\n" );
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document.write( "Hence,  cot(B) = \"cos%28B%29%2Fsin%28B%29\" = \"%28%28-1%2F4%29%29%2F%28%28-sqrt%2815%29%2F4%29%29\" = \"1%2Fsqrt%2815%29\" = \"sqrt%2815%29%2F15\".\r\n" );
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document.write( "ANSWER.  sin(B) = \"-sqrt%2815%29%2F4\",  cot(B) = \"sqrt%2815%29%2F15\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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