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

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

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2sin(θ)=-sqrt(3),0<= θ<2pi

2 sin (θ) = - 3, 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

2 sin (θ) = - 3, 0 \leq θ < 2 π

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

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}

cos^{2} (φ) = sin^{2} (φ)

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

sin (x) = \frac{1}{10}

(sin (θ) - 1) (sin (θ) + 1) = 0

5 sec (θ) - 6 = 0

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