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

Degrees

x = 20.90515 \dots^{\circ} + 18 0^{\circ} n, x = 69.09484 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 sin (2 x) = 2

Divide both sides by

3

3 sin (2 x) = 2

Divide both sides by

3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

2 x = arcsin (\frac{2}{3}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{2}{3}) + 2 πn

Divide both sides by

2

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

Simplify

x = \frac{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

2 x = π - arcsin (\frac{2}{3}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{2}{3}) + 2 πn

Divide both sides by

2

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

Simplify

x = \frac{π}{2} - \frac{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, cos (2 x) = 0

sec (θ) = \frac{3}{2}

6 cos (θ) + 3 = 0

sin^{2} (x) + 5 sin (x) + 6 = 0

- 6 tan^{2} (θ) + 11 tan (θ) - 6 = - 2 tan (θ)

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