solve 2sin^2 fata - 7 sinfata = -3 for fat, where 0<fata <= 360degress Show all steps to this question

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You should come up with the substitution `sin theta = y`  such that:

`2y^2 - 7y + 3 = 0`

You need to use quadratic formula to find `y_(1,2)`  such that:

`y_(1,2) = (7+-sqrt(49 - 24))/4`

`y_(1,2) = (7+-sqrt25)/4 =gt y_(1,2) = (7+-5)/4`

`y_(1) = 3 ; y_(2) = 1/2`

You need to find `theta`  such that:

`sin theta = 3`  is a contradiction since the values of sine function are not larger than 1.

`sin theta = 1/2 =gt theta = arcsin(1/2)`

`theta= 30^o`  and  `theta = 150^o`

Notice that the values for theta are in quadrants 1 and 2 since the values of sine function are positive in these quadrants.

Hence, the solutions to equation are `theta = 30^o`  and `theta = 150^o` .

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