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

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

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3sin(2x)=-2

3 sin (2 x) = - 2

x = - \frac{0.72972 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.72972 \dots}{2} + πn

Solution steps

3 sin (2 x) = - 2

Divide both sides by

3

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

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = - \frac{0.72972 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.72972 \dots}{2} + πn

x, arctan (y) = 2 arctan (x)

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

tan (x) = \frac{7.3}{6.8}

cot (θ) = \frac{13}{6}

cos (θ) = \frac{2}{6}

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