What is the general solution for 2sin(x-pi/3)+1=0 ?

The general solution for 2sin(x-pi/3)+1=0 is x=2pin+(3pi)/2 ,x=2pin+(13pi)/6

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2sin(x-pi/3)+1=0

2 sin (x - \frac{π}{3}) + 1 = 0

x = 2 πn + \frac{3 π}{2}, x = 2 πn + \frac{13 π}{6}

Solution steps

2 sin (x - \frac{π}{3}) + 1 = 0

Move

1

to the right side

2 sin (x - \frac{π}{3}) = - 1

Divide both sides by

2

sin (x - \frac{π}{3}) = - \frac{1}{2}

General solutions for

sin (x - \frac{π}{3}) = - \frac{1}{2}

x - \frac{π}{3} = \frac{7 π}{6} + 2 πn, x - \frac{π}{3} = \frac{11 π}{6} + 2 πn

Solve

x - \frac{π}{3} = \frac{7 π}{6} + 2 πn : x = 2 πn + \frac{3 π}{2}

Solve

x - \frac{π}{3} = \frac{11 π}{6} + 2 πn : x = 2 πn + \frac{13 π}{6}

x = 2 πn + \frac{3 π}{2}, x = 2 πn + \frac{13 π}{6}

cos (x) = 0.32

cos (4 t) = - \frac{3}{4}, 0 \leq t \leq 2 π

cos (x) = 0.71

cos (x) = 0.28

2 sin (θ) - 3 = - 2

What is the general solution for 2sin(x-pi/3)+1=0 ?
The general solution for 2sin(x-pi/3)+1=0 is x=2pin+(3pi)/2 ,x=2pin+(13pi)/6