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

The general solution for 2sin(x-pi/3)+sqrt(2)=0 is x=2pin+(19pi)/(12),x=2pin+(25pi)/(12)

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

2 sin (x - \frac{π}{3}) + 2 = 0

x = 2 πn + \frac{19 π}{12}, x = 2 πn + \frac{25 π}{12}

Solution steps

2 sin (x - \frac{π}{3}) + 2 = 0

Move

2

to the right side

2 sin (x - \frac{π}{3}) = - 2

Divide both sides by

2

sin (x - \frac{π}{3}) = - \frac{2}{2}

General solutions for

sin (x - \frac{π}{3}) = - \frac{2}{2}

x - \frac{π}{3} = \frac{5 π}{4} + 2 πn, x - \frac{π}{3} = \frac{7 π}{4} + 2 πn

Solve

x - \frac{π}{3} = \frac{5 π}{4} + 2 πn : x = 2 πn + \frac{19 π}{12}

Solve

x - \frac{π}{3} = \frac{7 π}{4} + 2 πn : x = 2 πn + \frac{25 π}{12}

x = 2 πn + \frac{19 π}{12}, x = 2 πn + \frac{25 π}{12}

sin^{2} (θ) + 3 = 2 cos^{2} (θ) + 4 sin (θ)

2 cos (2 x) + 3 = 4 cos (x)

sin (θ) = \frac{1}{4}, cos (θ)

2 sin^{2} (β) = 9 sin (β) - 4

4 cos^{2} (x) - 1 = 4, cos (2 x) - 1 = 0

What is the general solution for 2sin(x-pi/3)+sqrt(2)=0 ?
The general solution for 2sin(x-pi/3)+sqrt(2)=0 is x=2pin+(19pi)/(12),x=2pin+(25pi)/(12)