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

The general solution for 3sin^2(x)-2sin(x)=0 is x=0.72972…+2pin,x=pi-0.72972…+2pin,x=2pin,x=pi+2pin

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

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

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

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

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn, x = 2 πn, x = π + 2 πn

sin (u) = - \frac{2}{5}

2 sin (3 x) cos (2 x) - cos (2 x) = 0

\frac{1 + tan ( x )}{sin ( x )} = 0

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

x, cos (x y) = 0

What is the general solution for 3sin^2(x)-2sin(x)=0 ?
The general solution for 3sin^2(x)-2sin(x)=0 is x=0.72972…+2pin,x=pi-0.72972…+2pin,x=2pin,x=pi+2pin