document.write( "Question 731435: What is the exact value of tan345* \n" ); document.write( "
Algebra.Com's Answer #447134 by Edwin McCravy(20060)\"\" \"About 
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document.write( "We use the fact that 345° = 315°+30°, two special angles, and the identity\r\n" );
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document.write( "From our knowledge of special angles:\r\n" );
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document.write( "tan(315°) = -1 and tan(30°) = \"1%2Fsqrt%283%29\" = \"sqrt%283%29%2F3\"\r\n" );
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document.write( "tan(345°) = tan(315°+30°) =   = \"%28%28-1%29%2B%28sqrt%283%29%2F3%29%29%2F%281-%28-1%29%28sqrt%283%29%2F3%29%29\" = \"%28-1%2Bsqrt%283%29%2F3%29%2F%281%2Bsqrt%283%29%2F3%29\"\r\n" );
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document.write( "To simplify that, first we multiply top and bottom by 3 and distribute\r\n" );
document.write( "to clear of fractions in the numerator and denominator:\r\n" );
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document.write( "\"%283%28-1%2Bsqrt%283%29%2F3%29%29%2F%283%281%2Bsqrt%283%29%2F3%29%29\" = \"%28-3%2Bsqrt%283%29%29%2F%283%2Bsqrt%283%29%29\"\r\n" );
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document.write( "Now we rationalize the denominator by multiplying top and bottom by 3-√3,\r\n" );
document.write( "multiplying out and simplifying:\r\n" );
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document.write( " =  =  =  = \"%28-9%2B6sqrt%283%29-3%29%2F%289-3%29\" =\r\n" );
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document.write( "\"%28-12%2B6sqrt%283%29%29%2F6\" = \"%286%28-2%2Bsqrt%283%29%29%29%2F6\" = \"%28cross%286%29%28-2%2Bsqrt%283%29%29%29%2Fcross%286%29\" = -2+√3\r\n" );
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document.write( "It's always a good idea to check such answers with a calculator,\r\n" );
document.write( "getting and comparing the decimal approximations:\r\n" );
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document.write( "By calculator tan(345°) = -.2679491924\r\n" );
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document.write( "and by calculator\r\n" );
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document.write( "-2+√3 = -.2679491924\r\n" );
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document.write( "Edwin
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