document.write( "Question 979784: find the exact value of this expression: sin(tan^-1(-1)+sin^-1(1/2)) \n" ); document.write( "

Algebra.Com's Answer #601042 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "I read your writing   sin(tan^-1(-1)+sin^-1(1/2))   as\r
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\n" ); document.write( "\n" ); document.write( " $\"sin%28arctan%28-1%29+%2B+arcsin%281%2F2%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Do I read correctly?\r
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\n" ); document.write( "\n" ); document.write( "If my reading is correct, then the rest part is simple.\r
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\n" ); document.write( "\n" ); document.write( " $\"arcsin%281%2F2%29\"$ = $\"pi%2F6\"$ = 30°,\r
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\n" ); document.write( "\n" ); document.write( " $\"arctan%28-1%29\"$ = $\"-pi%2F4\"$ = -45°.\r
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\n" ); document.write( "\n" ); document.write( "sin(30° - 45°) = sin(30°)*cos(45°) - cos(30°)*sin(45°)       (subtraction formula for sines of Trigonometry, see the lesson Addition and subtraction formulas in this site)\r
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\n" ); document.write( "\n" ); document.write( "                      = $\"1%2F2\"$ . $\"sqrt%282%29%2F2\"$ - $\"sqrt%283%29%2F2\"$ . $\"sqrt%282%29%2F2\"$ = $\"sqrt%282%29%2F4\"$ - $\"sqrt%286%29%2F4\"$ = $\"%28sqrt%282%29-sqrt%286%29%29%2F4\"$ = $\"-%28sqrt%286%29-sqrt%282%29%29%2F4\"$ = -0.259.\r
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