Question

Find the solutions of the equation that are in the interval [0, 2pi)
sin(^2)x + 2 sinx - 8 = 0

So far I have sin(^2)x = 2(4 - sinx)

Answer 1

let sin(x)=a for convenience.

It doesn't seem like this quadratic equation can have any on extranous solutions

Answer 2

yo can try my thing let sin(x)=a,
but remember that for any value of x, \(\large\color{slate}{ -1\le {\rm Sin}(x)\le1 }\)

Answer 3

I mean any non extraneous solutions. it is a typo

Answer 4

Yes, it has to be within [0, 2pi] . No extraneous solutions

Answer 5

You should factor it and like solo said, replace sinx with a to make it easier on the eyes.

Answer 6

I factored it out and got a = -4. and a = 2. Neither of these are within the interval, so it has no solution!

Answer 7

extraneous solution is the one that doesn't work in the original equation.
non extraneous is the one that does work.

Answer 8

so no non-extraneous solutions you should say.

Answer 9

(double negative= positive, in my stetament)

Answer 10

Thank you for your help! :)

Answer 11

yw