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

The general solution for 2sin(x+pi/3)=-1 is x=2pin+(5pi)/6 ,x=2pin+(3pi)/2

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

2 sin (x + \frac{π}{3}) = - 1

x = 2 πn + \frac{5 π}{6}, x = 2 πn + \frac{3 π}{2}

Solution steps

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{5 π}{6}

Solve

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

x = 2 πn + \frac{5 π}{6}, x = 2 πn + \frac{3 π}{2}

cot^{2} (a) = cos^{2} (a) + cos (a) cos (a)

cot (x) \cdot tan (2 x) = 3

1 \cdot sin (3 5^{\circ}) = 1.33 \cdot sin (θ)

cos (3 A) = 1

cos (θ) = (- 0.68159)

What is the general solution for 2sin(x+pi/3)=-1 ?
The general solution for 2sin(x+pi/3)=-1 is x=2pin+(5pi)/6 ,x=2pin+(3pi)/2