What is the general solution for 4sin^2(x)+4sin(x)=-1 ?

The general solution for 4sin^2(x)+4sin(x)=-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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4sin^2(x)+4sin(x)=-1

4 sin^{2} (x) + 4 sin (x) = - 1

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

4 sin^{2} (x) + 4 sin (x) = - 1

Solve by substitution

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (θ) = \frac{8}{17}, cos (θ)

θ, 3 cos (θ - 5 5^{\circ}) = - 1.56

- 6 sin (c) - 12 = 2 sin (c) - 4

x, 3 cot^{2} (x) - 1 = 0

tan (2 x + 10) = cot (3 x - 15)

What is the general solution for 4sin^2(x)+4sin(x)=-1 ?
The general solution for 4sin^2(x)+4sin(x)=-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin