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

The general solution for sin(2x)=(2sqrt(2))/3 is x=(1.23095…)/2+pin,x= pi/2-(1.23095…)/2+pin

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sin(2x)=(2sqrt(2))/3

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

x = \frac{1.23095 \dots}{2} + πn, x = \frac{π}{2} - \frac{1.23095 \dots}{2} + πn

Solution steps

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

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = \frac{1.23095 \dots}{2} + πn, x = \frac{π}{2} - \frac{1.23095 \dots}{2} + πn

arccos (x) = \frac{15}{17}

4 tan^{2} (θ) - 9 = 0

sin (θ) = 7.19

3 = \frac{π}{3} sec^{2} (c)

\frac{sin ( 9 0 ^{\circ} )}{3.37} = \frac{sin ( x )}{0.7}

What is the general solution for sin(2x)=(2sqrt(2))/3 ?
The general solution for sin(2x)=(2sqrt(2))/3 is x=(1.23095…)/2+pin,x= pi/2-(1.23095…)/2+pin