What is the general solution for 2sin(θ)=-sqrt(3),360,180<= θ ?

The general solution for 2sin(θ)=-sqrt(3),360,180<= θ is No Solution for θ\in\mathbb{R}

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2sin(θ)=-sqrt(3),360,180<= θ

2 sin (θ) = - 3, 36 0^{\circ}, 18 0^{\circ} \leq θ

No Solution for θ \in R

Solution steps

2 sin (θ) = - 3, 36 0^{\circ}, 18 0^{\circ} \leq θ

Divide both sides by

2

2 sin (θ) = - 3

Divide both sides by

2

\frac{2 sin ( θ )}{2} = \frac{- 3}{2}

Simplify

sin (θ) = - \frac{3}{2}

sin (θ) = - \frac{3}{2}

General solutions for

sin (θ) = - \frac{3}{2}

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = 24 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

θ = 24 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

Solutions for the range

36 0^{\circ}

No Solution for θ \in R

tan (θ) = \frac{- 3}{4}

sin (2 x) cos (x) = cos (2 x) sin (x)

sin (x) = \frac{7}{12}

sin (x) = \frac{7}{13}

3 sin (x) - sin (x) - 3 = 0

What is the general solution for 2sin(θ)=-sqrt(3),360,180<= θ ?
The general solution for 2sin(θ)=-sqrt(3),360,180<= θ is No Solution for θ\in\mathbb{R}