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

The general solution for sin(x)=-2/3 is x=-0.72972…+2pin,x=pi+0.72972…+2pin

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sin(x)=-2/3

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

x = - 0.72972 \dots + 2 πn, x = π + 0.72972 \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 = - 0.72972 \dots + 2 πn, x = π + 0.72972 \dots + 2 πn

sin (4 x) = \frac{3}{2}

- 3 sin (x) = 0

csc^{2} (x) - 2 csc (x) = 2 - 4 sin (x)

2 cos^{2} (4 x) - 1 = 0

cos (θ) = - \frac{1}{2}

What is the general solution for sin(x)=-2/3 ?
The general solution for sin(x)=-2/3 is x=-0.72972…+2pin,x=pi+0.72972…+2pin