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

The general solution for solvefor x,sin(x)=-1/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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solvefor x,sin(x)=-1/2

solve for

x, sin (x) = - \frac{1}{2}

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

Degrees

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - \frac{1}{2}

General solutions for

sin (x) = - \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

sin (\frac{θ}{2}) = \frac{1}{2}

4 cos (θ) - 22 = 0

4 cos (4 x) = 0

4 sin^{3} (x) - 3 sin (x) = 0

cos (2 x) + sin (x) = 0, 0 \leq x \leq 2 π

What is the general solution for solvefor x,sin(x)=-1/2 ?
The general solution for solvefor x,sin(x)=-1/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin