document.write( "Question 1040921: Rewrite −3sin(x)−1cos(x) as Asin(x+ϕ)?\r
\n" ); document.write( "\n" ); document.write( "A:
\n" ); document.write( "ϕ: \r
\n" ); document.write( "\n" ); document.write( "When
\n" ); document.write( "-pi < ϕ < pi
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Algebra.Com's Answer #655912 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sin%28x%2By%29=sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"Asin%28x%29cos%28y%29=-3sin%28x%29\"$
\n" ); document.write( " $\"Acos%28y%29=-3\"$
\n" ); document.write( "and
\n" ); document.write( " $\"Acos%28x%29sin%28y%29=-1cos%28x%29\"$
\n" ); document.write( " $\"Asin%28y%29=-1\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"A%5E2%2Acos%5E2%28y%29%2BA%5E2%2Asin%5E2%28y%29=9%2B1\"$
\n" ); document.write( " $\"A%5E2=10\"$
\n" ); document.write( " $\"A=0+%2B-+sqrt%2810%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"tan%28y%29=%28Asin%28y%29%29%2F%28Acos%28y%29%29\"$
\n" ); document.write( " $\"tan%28y%29=-1%2F%28-3%29\"$
\n" ); document.write( " $\"y=0.322\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"-3sin%28x%29-cos%28x%29=-sqrt%2810%29%2Asin%28x%2B0.322%29\"$
\n" ); document.write( " $\"A=-sqrt%2810%29\"$
\n" ); document.write( " $\"phi=tan%5E%28-1%29%281%2F3%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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