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

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

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sin(2x)= 2/3

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

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

Solution steps

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

tan^{3} (θ) + tan^{2} (θ) - 3 tan (θ) - 3 = 0

x, sec (x) tan (x) = 0

csc (x) = \frac{1}{4}

3 sin (x) + 2 cos (x) = 1

tan (\frac{x}{2}) \cdot tan (x) = - 3

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