What is the general solution for sin(x)= 4/9 ?

The general solution for sin(x)= 4/9 is x=0.46055…+2pin,x=pi-0.46055…+2pin

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sin(x)= 4/9

sin (x) = \frac{4}{9}

x = 0.46055 \dots + 2 πn, x = π - 0.46055 \dots + 2 πn

Solution steps

sin (x) = \frac{4}{9}

Apply trig inverse properties

x = arcsin (\frac{4}{9}) + 2 πn, x = π - arcsin (\frac{4}{9}) + 2 πn

Show solutions in decimal form

x = 0.46055 \dots + 2 πn, x = π - 0.46055 \dots + 2 πn

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

- 4 sin (x) = 0

4 sin^{2} (θ) - sin (θ) - 4 = 0

tan (θ) = 1

sin (2 θ) + cos (2 θ) = 0

What is the general solution for sin(x)= 4/9 ?
The general solution for sin(x)= 4/9 is x=0.46055…+2pin,x=pi-0.46055…+2pin