`12sin^2 (x) - 13sin(x) + 3 = 0` Use the Quadratic Formula to solve the equation in the interval `0,2pi)`. Then use a graphing utility to approximate the angle `x`.

Expert Answers
gsarora17 eNotes educator| Certified Educator


using quadratic formula,





Solutions of sin(x)=1/3 for the range `0<=x<=2pi`

`x=arcsin(1/3) , x=pi-arcsin(1/3)`

Solutions of sin(x)=3/4 for the range are,

`x=arcsin(3/4) , x=pi-arcsin(3/4)`

Solutions are `x=arcsin(1/3) , arcsin(3/4) , pi-arcsin(1/3) , pi-arcsin(3/4)`

See the attached graph,

x `~~` 0.3 , 0.8 , 2.3 , 2.8

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