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Solve 11 sin^2 = 13 -3 sin^2 y for y, where 0 is greater or equal to y < 360...

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dumbmath | Student, Undergraduate | (Level 1) Honors

Posted March 29, 2012 at 4:08 AM via web

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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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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted March 29, 2012 at 4:19 AM (Answer #1)

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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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