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

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

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2sin^2(x)+3sin(x)=0

2 sin^{2} (x) + 3 sin (x) = 0

x = 2 πn, x = π + 2 πn

Solution steps

2 sin^{2} (x) + 3 sin (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = - \frac{3}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

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

arccos (x) + 2 arcsin (\frac{3}{2}) = π

3 - 3 sin (θ) = 2 cos^{2} (θ)

tan (a) = - 3

cos^{2} (θ) = sin^{2} (θ)

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