Finding roots of 3 sin^3 (x) + 5 sin^2 (x) - 2 sin(x) = 0 on (-pi, pi)

how do i determine the roots of 3 sin (cubed) x+5sin (squared) x-2sinx=0 on a (-pi,+pi) scale!

What have you done, so far? Where are you stuck?

I'd begin by factoring the left-hand side of the given equation.

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Gr12math said:

how do i determine the roots of 3 sin (cubed) x+5sin (squared) x-2sinx=0 on a (-pi,+pi) scale?

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I'm not sure what you mean by "on a (-pi, +pi) scale"...? Do you perhaps mean "on the interval from \(\displaystyle -\pi\) to \(\displaystyle +\pi,\), not including the endpoints"...? If so, please confirm. If not, please correct.

As for how to find the roots of the equation, use the usual methods, like they gave you in class and in your book. For this particular equation:

You first noted that this is a quadratic in sin(x). You factored and created the two resulting (but simpler) trig equations. Then, using what you've memorized for standard angle values, etc, you solved each of the simpler equations (at least on the first quadrant), and... then what?

Please be complete. Thank you!