Question

Question #1bd0f

Answer 1

`theta=30°`, `or theta = 150°`

Explanation:

`2sin^2theta-sintheta=0`

or, `sintheta(2sintheta-1)=0` [taking `sintheta` common from both sides]

now,either `sintheta=0` or `(2sintheta-1)=0`

we know the value of `sintheta` being `0` is `0` degree.so that rules out because the domain is `0 < theta < 360.`

now `(2sintheta-1)=0`

or `2sintheta=1`
so `sintheta=1/2`
the value of `sintheta` being `1/2` is `30` degree.

So the first value is `30`. This is in the first quadrant, but we know `sin theta` is positive in the second quadrant too. So we take `180` degrees. We can't take 90 degrees because that would change sin to cos. So now the equation is:

`sin30=sin(180-30)`

`sin30=sin150`

so this is the answer.

Answer: `sin30°`, `sin150°`