Question

Solve (degrees):

3sin^2(x)-11sin(x)-4=0

It's just a quadratic but doesnt wprk?

Answer 1

quadratics always work. Maybe it just doesn't factor easily.

Nope. works just fine:

(3sinx+1)(sinx-4) = 0

Now just evaluate sinx so you get solutions for x.

Answer 2

How do I evaluate sinx-4 since I can't do arcsin4. How do I interpret that?

Answer 3

aha!
That means that while sinx=4 is a "solution" to the polynomial, it is not a real solution. It is extraneous, due to the properties of sin(x)

Answer 4

true, sinx = 4 has no solution.

Many equations have extraneous roots, so they don't become part of your solution set

In this case the only factor that works is
3sinx + 1 = 0
sinx = -1/3
so x is in the third or fourth quadrant according to the CAST rule
the angle in standard position is appr 19.47°
(sin 19.47 = +1/3)
x = 180°+19.47° = 199.47° or
x = 360-19.47 = 340.53°

of course don't forget that the period of sinx is 360°
so adding or subtracting multiple of 360° to any answer will yield a new answer.
in general:
x = (199.47 + 360k)° or
x = (340.53 + 360k)°, where k is an integer