document.write( "Question 1159666: Use the given conditions to find the exact value of the expression.
\n" ); document.write( "sin α = − 5/13, tan α > 0, sin (α − 5π/3)\r
\n" ); document.write( "\n" ); document.write( "I got 5+ $\"sqrt%283%29\"$ /3 which is wrong. \r
\n" ); document.write( "\n" ); document.write( "This is my work:
\n" ); document.write( "cos a=- $\"sqrt%281-sin%5E2+%28theta%29%29\"$ = 12/13\r
\n" ); document.write( "\n" ); document.write( "b= -5pi/3 which is has the values (-1/2) for cosb and ( $\"sqrt%283%29\"$ /2 for sinb.
\n" ); document.write( "I use sin(a-b) formula= sinAcosB+cosAsinB
\n" ); document.write( "= (-5/13)(-1/2)+(12/13)( $\"sqrt%283%29\"$ /2)= 5+12 $\"sqrt%283%29\"$ /36 = 5+ $\"sqrt%283%29\"$ /3 or am I not suppose to simplify the 12 and 36? \r
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Algebra.Com's Answer #782733 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


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document.write( "In sin(a-b) = sin(a)cos(b)-cos(a)sin(b), the minus sign is provided, so
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document.write( "b is not -5pi/3;  instead,  it is simply 5pi/3  [ it might help to think of it as a pattern match. You are subtracting one angle from another, but both those angles have their own signs. ]\r
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document.write( "cos(b) is 
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document.write( "sin(b) is -\r
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document.write( "resulting in 
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document.write( "Although you had the sign error, there was also an error in how you simplified the expression-- you somehow lost the 1/26 from the first term.  Note that sin() and cos() will always produce outputs between -1 and +1 inclusive.  The \"5+\" in your answer is an immediate indication that something is wrong. \r
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document.write( "But, I want to congratulate you on your effort.  Not many students post their work here and it is refreshing to see... AND an \"A\" for your approach.  \r
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document.write( "EDIT: I fixed the sin(a-b) formula and two missing minus signs, result is the same.\r
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