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

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

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

sin (\frac{π}{3} - x) = \frac{1}{2}

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

Solution steps

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}

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

0.1 cos (x) + 0.45 sin (x) = 0.3125

2 sin (2 x) cos (3 x) + cos (3 x) = 0

cos^{2} (x) - 3 sin^{2} (x) = - 2

- 1 + sin (θ) = - 1

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