document.write( "Question 366464: Find all values of theta in the interval 0°< theta <360° that satisfy the equation 2(sin theta +csc theta)=5 \n" ); document.write( "

Algebra.Com's Answer #261150 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sin+%28theta%29+%2B+csc+%28theta%29+=+5%2F2\"$ ,
\n" ); document.write( " $\"sin+%28theta%29+%2B1%2Fsin+%28theta%29+=+5%2F2\"$ ,
\n" ); document.write( " $\"%28%28sin+%28theta%29%29%5E2+%2B1%29%2Fsin%28theta%29+=+5%2F2\"$ ,
\n" ); document.write( " $\"2%28sin+%28theta%29%29%5E2+%2B2=+5sin%28theta%29+\"$ ,
\n" ); document.write( " $\"2%28sin+%28theta%29%29%5E2+-+5sin%28theta%29%2B2=+0\"$ ,
\n" ); document.write( " $\"%282sin%28theta%29-1%29%28sin%28theta%29-2%29+=+0\"$ . The first factor gives
\n" ); document.write( " $\"2sin%28theta%29+=+1\"$ , or $\"sin%28theta%29=1%2F2\"$ , giving $\"theta\"$ = 30 or 150 degrees.
\n" ); document.write( "The second factor $\"sin%28theta%29-2+=+0\"$ does not give any solutions. (Why?) \n" ); document.write( "

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