What is the general solution for 2sin(θ)+sqrt(3)=0 ?

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

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2sin(θ)+sqrt(3)=0

2 sin (θ) + 3 = 0

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

Degrees

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

Solution steps

2 sin (θ) + 3 = 0

Move

3

to the right side

2 sin (θ) + 3 = 0

Subtract

3

from both sides

2 sin (θ) + 3 - 3 = 0 - 3

Simplify

2 sin (θ) = - 3

2 sin (θ) = - 3

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

cos (2 x) = \frac{1}{2}

cos^{2} (x) = 2 + 2 sin (x)

arccsc (\frac{2 3}{3})

csc (θ) + 2 = 0

csc (x) = 2

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