document.write( "Question 958137: If possible, find a solution to tan(2θ+7)=−11 . If no solution exists, enter NONE. \n" ); document.write( "

Algebra.Com's Answer #585656 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"tan%282%2Atheta%2B7%29+=+-11\"$
\n" ); document.write( "If all you need is one solution (there are infinitely many), then all you need to do is...
\n" ); document.write( "Find the inverse tan of each side:
\n" ); document.write( "tan^-1( $\"tan%282%2Atheta%2B7%29\"$ ) = tan^-1(-11)
\n" ); document.write( "The left side simplies and the calculator will give us an number for the right side:
\n" ); document.write( " $\"2%2Atheta%2B7\"$ = -84.8 (degrees, rounded-off)
\n" ); document.write( "Now subtract 7 from each side:
\n" ); document.write( " $\"2%2Atheta\"$ = -91.8 (degrees, rounded-off)
\n" ); document.write( "And divide by two:
\n" ); document.write( " $\"theta\"$ = -45.9 (degrees, rounded-off)

\n" ); document.write( "All the other solutions will be multiples of 180 (since the period of tan is 180) away from -45.9.

\n" ); document.write( "In response to the question in your \"Thank you\" note:
\n" ); document.write( "To turn -45.9 into radians:
\n" ); document.write( " $\"-45.9+%2A+%28pi%2F180%29+=+-0.255%2Api\"$
\n" ); document.write( "If this is not the answer provided, then try adding various multiples of $\"pi\"$ (since the period of tan, in radians, is $\"pi\"$ ) until you get the answer. For example:
\n" ); document.write( " $\"-0.255%2Api%2Bpi+=+0.745%2Api\"$

\n" ); document.write( " $\"-0.255%2Api%2B2%2Api+=+1.745%2Api\"$

\n" ); document.write( "If the \"official\" answer does not have $\"pi\"$ in it, then replace $\"pi\"$ with 3.141529 (or some rounded-off version of this decimal). \n" ); document.write( "

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