What is the general solution for sin(2x)-2/3 =0 ?

The general solution for sin(2x)-2/3 =0 is x=(0.72972…)/2+pin,x= pi/2-(0.72972…)/2+pin

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sin(2x)-2/3 =0

sin (2 x) - \frac{2}{3} = 0

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

sin (2 x) - \frac{2}{3} = 0

Move

\frac{2}{3}

to the right side

sin (2 x) - \frac{2}{3} = 0

Add

\frac{2}{3}

to both sides

sin (2 x) - \frac{2}{3} + \frac{2}{3} = 0 + \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

2 sin (θ) + cos (2 θ) = 0

sin (x + \frac{π}{4}) = 2 cos (x + \frac{π}{4})

5 = 7 cos (\frac{π}{3} t)

6 cos^{2} (x) - 4 = 0

csc (x) = 3.5

What is the general solution for sin(2x)-2/3 =0 ?
The general solution for sin(2x)-2/3 =0 is x=(0.72972…)/2+pin,x= pi/2-(0.72972…)/2+pin