5sin^2x+3sinx=4 - Math Central

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Question from Chris:

I have been trying to answer this question and i have finally got an answer could somebody please tell me if im right or wrong and if wrong show me the errors of my ways
Thanks chris
solve the following in the range 0 - 360 degrees?
5sin^2x+3sinx=4
5sin^2x+3sinx-4=0
5sinx+2=0
sinx=-2/5=-0.4
x=sin^-1 (0.4)
x=203,35 or 336,25
and sinx-1 = 0
sinx=1
x=sin^-1
So x=90
Please help?

Chris,

You have the equation

5sin²x+3sinx-4=0

What you need to see is that this is a quadratic equation in disguise. Let y = sin(x) then the equation is

5y² + 3y - 4 = 0

Solve the equation for x either by using the general quadratic expression or by completing the square. Once you have y you can find x using y = sin(x).

Penny

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