Solve (degrees):
3sin^2(x)-11sin(x)-4=0
It's just a quadratic but doesnt wprk?
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.
How do I evaluate sinx-4 since I can't do arcsin4. How do I interpret that?
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)
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
To solve the quadratic equation 3sin^2(x) - 11sin(x) - 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, the coefficient of sin^2(x) is 3, the coefficient of sin(x) is -11, and the constant term is -4. Plugging these values into the quadratic formula, we have:
x = (11 ± √((-11)^2 - 4*3*(-4))) / (2*3)
Simplifying the expression inside the square root:
x = (11 ± √(121 + 48)) / 6
x = (11 ± √(169)) / 6
x = (11 ± 13) / 6
This gives us two possible solutions:
1. x = (11 + 13) / 6 = 4
2. x = (11 - 13) / 6 = -1/3
Therefore, the solutions for the equation 3sin^2(x) - 11sin(x) - 4 = 0 are x = 4 and x = -1/3.
If you mentioned that the quadratic formula did not work, it is possible that there was a mistake in the calculations or derivation. In that case, it would be helpful to check the calculations again or try an alternative method to solve the equation.