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

Degrees

x = - 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 221.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

Apply trig inverse properties

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

General solutions for

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

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

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

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

4 + 4 cos (x) = - 6 cos (x)

2 cos (\frac{x}{2}) = 3, 0 \leq x \leq 2 π

sin (A) = \frac{4}{5}

3 tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

sin (2 x) = 4 cos (x)

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