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

Degrees

x = 35.26438 \dots^{\circ} + 18 0^{\circ} n, x = 54.73561 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

2 x = arcsin (\frac{2 2}{3}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{2 2}{3}) + 2 πn

Divide both sides by

2

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

Simplify

x = \frac{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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

x = \frac{π}{2} - \frac{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