What is the general solution for 4sin(θ)+2sqrt(3)=0,0<= θ<= 360 ?

The general solution for 4sin(θ)+2sqrt(3)=0,0<= θ<= 360 is θ=240,θ=300

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4sin(θ)+2sqrt(3)=0,0<= θ<= 360

4 sin (θ) + 23 = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

θ = 24 0^{\circ}, θ = 30 0^{\circ}

Radians

θ = \frac{4 π}{3}, θ = \frac{5 π}{3}

Solution steps

4 sin (θ) + 23 = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

Move

23

to the right side

4 sin (θ) + 23 = 0

Subtract

23

from both sides

4 sin (θ) + 23 - 23 = 0 - 23

Simplify

4 sin (θ) = - 23

4 sin (θ) = - 23

Divide both sides by

4

4 sin (θ) = - 23

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{- 2 3}{4}

Simplify

\frac{4 sin ( θ )}{4} = \frac{- 2 3}{4}

Simplify

\frac{4 sin ( θ )}{4} : sin (θ)

\frac{4 sin ( θ )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (θ)

Simplify

\frac{- 2 3}{4} : - \frac{3}{2}

\frac{- 2 3}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 3}{4}

Cancel the common factor:

2

= - \frac{3}{2}

sin (θ) = - \frac{3}{2}

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

0 \leq θ \leq 36 0^{\circ}

θ = 24 0^{\circ}, θ = 30 0^{\circ}

(1.33) sin (2 5^{\circ}) = (1.5) sin (θ)

cos (y) = - \frac{1}{2}

\frac{2}{1 + sin ( x )} = 3 - 2 sin (x)

x, 4 cos^{2} (x) = 5 + 4 sin (x)

t, y = cos (2 t)

What is the general solution for 4sin(θ)+2sqrt(3)=0,0<= θ<= 360 ?
The general solution for 4sin(θ)+2sqrt(3)=0,0<= θ<= 360 is θ=240,θ=300