What is the general solution for sin(x)=(sqrt(2))/3 ?

The general solution for sin(x)=(sqrt(2))/3 is x=0.49088…+2pin,x=pi-0.49088…+2pin

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sin(x)=(sqrt(2))/3

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

x = 0.49088 \dots + 2 πn, x = π - 0.49088 \dots + 2 πn

Solution steps

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

Apply trig inverse properties

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

Show solutions in decimal form

x = 0.49088 \dots + 2 πn, x = π - 0.49088 \dots + 2 πn

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

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

0 = ((10 cos (x)) - 8)^{2} ((10 sin (x)) - 6)^{2}

tan (x) = \frac{4}{2}

- 6 cos (x) = 2 - 2 cos (x)

What is the general solution for sin(x)=(sqrt(2))/3 ?
The general solution for sin(x)=(sqrt(2))/3 is x=0.49088…+2pin,x=pi-0.49088…+2pin