What is the general solution for sin(θ)=-(sqrt(3))/2 ,0<= θ<2pi ?

The general solution for sin(θ)=-(sqrt(3))/2 ,0<= θ<2pi is θ=(4pi)/3 ,θ=(5pi)/3

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sin(θ)=-(sqrt(3))/2 ,0<= θ<2pi

sin (θ) = - \frac{3}{2}, 0 \leq θ < 2 π

θ = \frac{4 π}{3}, θ = \frac{5 π}{3}

Degrees

θ = 24 0^{\circ}, θ = 30 0^{\circ}

Solution steps

sin (θ) = - \frac{3}{2}, 0 \leq θ < 2 π

General solutions for

sin (θ) = - \frac{3}{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}

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solutions for the range

0 \leq θ < 2 π

θ = \frac{4 π}{3}, θ = \frac{5 π}{3}

sin (x) = 7938894612

3 sin (2 θ) = 5 cos (θ)

cos (2 x) = \frac{1}{2}, (0, 2 π)

3 sec (x) = 6

6 = 6 sin (2 π (47) t), 0 < t < 0.0212

What is the general solution for sin(θ)=-(sqrt(3))/2 ,0<= θ<2pi ?
The general solution for sin(θ)=-(sqrt(3))/2 ,0<= θ<2pi is θ=(4pi)/3 ,θ=(5pi)/3