What is the general solution for sin(x)=-1/3 ?

The general solution for sin(x)=-1/3 is x=-0.33983…+2pin,x=pi+0.33983…+2pin

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sin(x)=-1/3

sin (x) = - \frac{1}{3}

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

Solution steps

sin (x) = - \frac{1}{3}

Apply trig inverse properties

x = arcsin (- \frac{1}{3}) + 2 πn, x = π + arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = - 0.33983 \dots + 2 πn, x = π + 0.33983 \dots + 2 πn

5 cot (x) + 5 = 0

tan (x) + 1 = 2

cot (x) sec (x) + cot (x) = 0

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

cos (2 θ) - cos (θ) = 0

What is the general solution for sin(x)=-1/3 ?
The general solution for sin(x)=-1/3 is x=-0.33983…+2pin,x=pi+0.33983…+2pin