What is the general solution for 3sin^2(x)=-7sin(x)-4,0<= x<= 2pi ?

The general solution for 3sin^2(x)=-7sin(x)-4,0<= x<= 2pi is x=(3pi)/2

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3sin^2(x)=-7sin(x)-4,0<= x<= 2pi

3 sin^{2} (x) = - 7 sin (x) - 4, 0 \leq x \leq 2 π

x = \frac{3 π}{2}

Solution steps

3 sin^{2} (x) = - 7 sin (x) - 4, 0 \leq x \leq 2 π

Solve by substitution

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

sin (x) = - 1, 0 \leq x \leq 2 π : x = \frac{3 π}{2}

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

No Solution

Combine all the solutions

x = \frac{3 π}{2}

sin (- θ) = sin (θ)

4 cos^{2} (x) + 4 cos (x) = 3

sec (2 x) csc (2 x) = 2 csc (2 x)

3 cos (x) tan (x) = - 10 tan (x)

sin (x) cos (x) + cos (x) = 0

What is the general solution for 3sin^2(x)=-7sin(x)-4,0<= x<= 2pi ?
The general solution for 3sin^2(x)=-7sin(x)-4,0<= x<= 2pi is x=(3pi)/2