What is the general solution for 3sin^2(x)-sin(x)-4=0 ?

The general solution for 3sin^2(x)-sin(x)-4=0 is x=(3pi)/2+2pin

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

3 sin^{2} (x) - sin (x) - 4 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

3 sin^{2} (x) - sin (x) - 4 = 0

Solve by substitution

sin (x) = \frac{4}{3}, sin (x) = - 1

sin (x) = \frac{4}{3} :

No Solution

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

sin (3 x) = sin^{2} (x)

2 cot (x) + 3 = 0

cos (x + 6 0^{\circ}) + sin (x) = 0

sin (x) \cdot cos (x) = \frac{1}{4}

sin (θ) = \frac{- 3}{2}, 0 \leq θ \leq 4 π

What is the general solution for 3sin^2(x)-sin(x)-4=0 ?
The general solution for 3sin^2(x)-sin(x)-4=0 is x=(3pi)/2+2pin