What is the general solution for sin(x)=(sqrt(3))/3 ?

The general solution for sin(x)=(sqrt(3))/3 is x=0.61547…+2pin,x=pi-0.61547…+2pin

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sin(x)=(sqrt(3))/3

sin (x) = \frac{3}{3}

x = 0.61547 \dots + 2 πn, x = π - 0.61547 \dots + 2 πn

Solution steps

sin (x) = \frac{3}{3}

Apply trig inverse properties

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

Show solutions in decimal form

x = 0.61547 \dots + 2 πn, x = π - 0.61547 \dots + 2 πn

cos (2 θ) = - \frac{1}{2}, 0 \leq θ < 2 π

tan (x) tan (2 x) = 1

2 sin^{2} (x) + 7 sin (x) = 4

22 cos (θ) + 4 = 6

sin (x) + cos (x) = \frac{1}{2}

What is the general solution for sin(x)=(sqrt(3))/3 ?
The general solution for sin(x)=(sqrt(3))/3 is x=0.61547…+2pin,x=pi-0.61547…+2pin