Question

Find solution of the equation 3sin^2x-7sinx+2=0

Answer 1

We can factor, or simply use quadratic formula to solve for \(\sin x\):
\[
(\sin x-2)(3\sin x-1)=0
\]So, we know:\[
\sin x\ne2
\]So, therefore:
\[
3\sin x=1\implies\\
\sin x=\frac{1}{3}\implies\\
x=\sin^{-1}\frac{1}{3}
\]And we are done.

Answer 2

Thanks but it has an interval of [0,2pi]
would that be the answer even though it has an interval

Answer 3

Well, we have two values for such:
\[
x=\pi-\sin^{-1}\left(\frac{1}{3}\right)\\
x=\sin^{-1}\left(\frac{1}{3}\right)
\]Where:
\[
x\in[0, 2\pi)
\]

Answer 4

Thanks so what r the two values for such and solution. Could u elaborate some more so i can fully understand.

Answer 5

The hint that they gave us for such question is :

To solve this problem you will have to use the quadratic formula, inverse trigonometric functions and the symmetry of the unit circle.
Also, you should look at the graph of the sine function over the interval[0,2pi]

Answer 6

Those are the two values. The quadratic formula is not necessary as we simply factored, and we notice that, if we draw a line on a sinusoidal graph, the two possible solutions to such intersection lie at \(a\) and \(\pi-a\). There is no nice expression for the value of \(\sin^{-1}\frac{1}{3}\)

Answer 7

ok thanks a lot for your help

Answer 8

Sure thing.