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

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

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

2 sin (\frac{π}{3} - x) - 1 = 0

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

Solution steps

2 sin (\frac{π}{3} - x) - 1 = 0

Move

1

to the right side

2 sin (\frac{π}{3} - x) = 1

Divide both sides by

2

sin (\frac{π}{3} - x) = \frac{1}{2}

General solutions for

sin (\frac{π}{3} - x) = \frac{1}{2}

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

Solve

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

Solve

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

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

- 2 sin (x) - 1 = 0

- 3 = cot^{2} (θ) + 3 csc (θ)

arccos (e^{- x}) = \frac{π}{3}

cos (θ) = - \frac{11}{170}

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0, 0 \leq θ \leq 2 π

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