Given that 0≤β<2π, which of the following gives all solutions to the equation 2sin2β=9sinβ−4?

We know the following equation:

So we can write this equation as two function that are equalized, that is:

So let's solve this equation graphically. We know that:

And this interval is indicated with the two vertical lines drawn in red below. For this graph the x-axis represents β.

So the β-values of the graph of f(β) that makes this function to be zero are:

And those two values lies on the given interval.

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Step-by-step explanation:

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