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

The general solution for 2sin((2x)/3)-sqrt(2)=0 is x=(3pi)/8+3pin,x=(9pi)/8+3pin

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2sin((2x)/3)-sqrt(2)=0

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

x = \frac{3 π}{8} + 3 πn, x = \frac{9 π}{8} + 3 πn

Solution steps

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

Move

2

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{2 x}{3} = \frac{π}{4} + 2 πn, \frac{2 x}{3} = \frac{3 π}{4} + 2 πn

Solve

\frac{2 x}{3} = \frac{π}{4} + 2 πn : x = \frac{3 π}{8} + 3 πn

Solve

\frac{2 x}{3} = \frac{3 π}{4} + 2 πn : x = \frac{9 π}{8} + 3 πn

x = \frac{3 π}{8} + 3 πn, x = \frac{9 π}{8} + 3 πn

tan (θ) = - \frac{1}{4}

\frac{1}{cos ( x ) + 1} + \frac{1}{cos ( x ) - 1} = 2 csc (x) cot (x)

3 - sin (θ) = cos (2 θ)

tan (θ) = \frac{- 1}{1}

cot (x) = 3

What is the general solution for 2sin((2x)/3)-sqrt(2)=0 ?
The general solution for 2sin((2x)/3)-sqrt(2)=0 is x=(3pi)/8+3pin,x=(9pi)/8+3pin