Solve 11 sin^2 = 13 -3 sin^2 y for y, where 0 is greater or equal to y < 360 degrees, how many angles satisfy this equation?

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You need to move all terms containing to the left side such that:

`11 sin^2 y + 3 sin^2 y = 13`

`14 sin^2 y = 13 =gt sin^2 y = 13/14`

`sin y = +- sqrt(13/14)`

`y = arcsin(13/14) = 68.12^o` if `y in (0,90^o)` or `y =111.88^o` if `y in (90^o,180^o)`

`y =248.12^o` if `y in (180^o,270^o)` or `y = 291.88^o` if `y in (270^o, 360^o)`

**Hence, the solutions to equation are `y = 68.12^o;y = 111.88^o;y = 248.12^o;y = 291.88^o.` **

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