What is the general solution for sin(x)= 4/(6sqrt(2)) ?

The general solution for sin(x)= 4/(6sqrt(2)) is x=0.49088…+2pin,x=pi-0.49088…+2pin

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sin(x)= 4/(6sqrt(2))

sin (x) = \frac{4}{6 2}

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

Solution steps

sin (x) = \frac{4}{6 2}

Simplify

\frac{4}{6 2} : \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

cos (5 x) = cos (3 x)

2 cos (2 t) = 0

4 cos^{2} (θ) = 3 + 3 sin (θ)

4 cos (3 θ) + 23 = 0

cos (2 θ) + 3 cos (θ) - 1 = 0

What is the general solution for sin(x)= 4/(6sqrt(2)) ?
The general solution for sin(x)= 4/(6sqrt(2)) is x=0.49088…+2pin,x=pi-0.49088…+2pin