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

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

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

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

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

Solution steps

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

Solve by substitution

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

sin (x) = - 2 :

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

100 = 100 + 40 sin (\frac{9 π}{4} t)

tan (φ) = - \frac{1}{3}

sin (3 m) = 0

cos (a) = - \frac{8}{17}, sin (b) = \frac{3}{5}

7 tan (θ) + 9 = 0

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