Question

2 sin squared theta minus 5 sin theta + 2 is greater than zero theta belong to 0 to 360

Answer 1

2 sin^2 @ - 5 sin @ + 2 > 0 [0,2π]

2 sin ^2 @ - 4 sin @ - sin @ + 2 > 0

2 sin @ ( sin @ - 2 ) - 1 ( sin @ - 2 ) > 0

( 2 sin @ - 1 ) ( sin @ - 2 ) > 0

then

2 sin @ - 1 > 0

sin @ > 1/2

@ > π / 6 , 5π / 6

and

2 sin @ > 2

sin @ > 2 ( not possible)

because ;

-1 < sin @ < 1 ( always )





so then interval

[ 0 , π/6 ) U ( 5π/6 , 2π ]

Answer 2

Hope this helps you.