What is the general solution for -2sin^2(x)-5sin(x)=-3 ?

The general solution for -2sin^2(x)-5sin(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin

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-2sin^2(x)-5sin(x)=-3

- 2 sin^{2} (x) - 5 sin (x) = - 3

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

- 2 sin^{2} (x) - 5 sin (x) = - 3

Solve by substitution

sin (x) = - 3, sin (x) = \frac{1}{2}

sin (x) = - 3 :

No Solution

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

b, a = cos (- 1 (\frac{a}{a ^{2} + b ^{2}}))

(\frac{1}{2} sin (2 x))^{2} = \frac{1}{4} sin^{2} (4 x)

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

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

6 sin (x) + 12 = 15

What is the general solution for -2sin^2(x)-5sin(x)=-3 ?
The general solution for -2sin^2(x)-5sin(x)=-3 is x= pi/6+2pin,x=(5pi)/6+2pin