document.write( "Question 1042080: If cosθ=−1/3 and θ is in the interval [π, 3π/2], then find the value of sin(θ). \n" ); document.write( "

Algebra.Com's Answer #656986 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the Pythagorean Trig Identity to solve for $\"sin%28theta%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28theta%29+%2B+cos%5E2%28theta%29+=+1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28theta%29+%2B+%28cos%28theta%29%29%5E2+=+1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28theta%29+%2B+%28-1%2F3%29%5E2+=+1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28theta%29+%2B+1%2F9+=+1\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28theta%29+%2B+1%2F9-1%2F9+=+1-1%2F9\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28theta%29+=+9%2F9-1%2F9\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%5E2%28theta%29+=+8%2F9\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28sin%5E2%28theta%29%29+=+sqrt%288%2F9%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"abs%28sin%28theta%29%29+=+sqrt%288%2F9%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%28theta%29+=+%22%22%2B-sqrt%288%2F9%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%28theta%29+=+-sqrt%288%2F9%29\"$ See note below\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%28theta%29+=+-%28sqrt%288%29%29%2F%28sqrt%289%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%28theta%29+=+-%28sqrt%288%29%29%2F%283%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%28theta%29+=+-%28sqrt%284%2A2%29%29%2F%283%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%28theta%29+=+-%28sqrt%284%29%2Asqrt%282%29%29%2F%283%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"sin%28theta%29+=+-%282%2Asqrt%282%29%29%2F%283%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "θ is in the interval [π, 3π/2], so theta is in quadrant 3 where sine is negative. \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"sin%28theta%29%3C0\"$ which means we can drop the plus/minus and focus solely on the minus. \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The final answer is $\"sin%28theta%29+=+-%282%2Asqrt%282%29%29%2F%283%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );