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

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

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3sin(x)=-2

3 sin (x) = - 2

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

Solution steps

3 sin (x) = - 2

Divide both sides by

3

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

6 sin (x) + 1 = 4 sin (x)

5 \cdot 10 cos (x) = 48

5 sin (x) - 1 = 2 cos^{2} (x)

tan^{2} (x) + 23 tan (x) + 3 = 0

7 tan (θ) - 8 = 5 tan (θ) - 5

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