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

The general solution for sin(θ)=(sqrt(3))/2 ,cos(θ)<0,0<θ<2pi is No Solution for θ\in\mathbb{R}

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sin(θ)=(sqrt(3))/2 ,cos(θ)<0,0<θ<2pi

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

No Solution for θ \in R

Solution steps

sin (θ) = \frac{3}{2}, cos (θ) < 0, 0 < 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{π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn

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

Solutions for the range

cos (θ) < 0

No Solution for θ \in R

tan (x) = 1, 0 \leq x < 2 π

x, sin (2 x) \cdot cos (2 x) = 0.5

2 sin^{2} (x) + sin (x) - 3 = 0, 6

(1 - sin (2 x)) \cdot (1 - cos^{2} (x)) = 0

5 cos (x) - 10 sin (x) cos (x) = 0, 0 \leq x \leq \frac{π}{2}

What is the general solution for sin(θ)=(sqrt(3))/2 ,cos(θ)<0,0<θ<2pi ?
The general solution for sin(θ)=(sqrt(3))/2 ,cos(θ)<0,0<θ<2pi is No Solution for θ\in\mathbb{R}