What is the general solution for sin(x)=-8/9 ?

The general solution for sin(x)=-8/9 is x=-1.09491…+2pin,x=pi+1.09491…+2pin

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sin(x)=-8/9

sin (x) = - \frac{8}{9}

x = - 1.09491 \dots + 2 πn, x = π + 1.09491 \dots + 2 πn

Solution steps

sin (x) = - \frac{8}{9}

Apply trig inverse properties

x = arcsin (- \frac{8}{9}) + 2 πn, x = π + arcsin (\frac{8}{9}) + 2 πn

Show solutions in decimal form

x = - 1.09491 \dots + 2 πn, x = π + 1.09491 \dots + 2 πn

cos^{2} (θ) + 2 cos (θ) = 3

cos^{2} (x) = \frac{1}{9}

sin^{4} (x) = sin^{4} (x) cos (x)

csc^{2} (θ) + cot (θ) = - 2

sec (x) csc (x) = csc (x)

What is the general solution for sin(x)=-8/9 ?
The general solution for sin(x)=-8/9 is x=-1.09491…+2pin,x=pi+1.09491…+2pin