What is the general solution for sin(x)=(-sqrt(3))/2 ,270<x<360 ?

The general solution for sin(x)=(-sqrt(3))/2 ,270<x<360 is x=300

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sin(x)=(-sqrt(3))/2 ,270<x<360

sin (x) = \frac{- 3}{2}, 27 0^{\circ} < x < 36 0^{\circ}

x = 30 0^{\circ}

Radians

x = \frac{5 π}{3}

Solution steps

sin (x) = \frac{- 3}{2}, 27 0^{\circ} < x < 36 0^{\circ}

Apply the fraction rule:

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

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

General solutions for

sin (x) = - \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}

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

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

Solutions for the range

27 0^{\circ} < x < 36 0^{\circ}

x = 30 0^{\circ}

What is the general solution for sin(x)=(-sqrt(3))/2 ,270<x<360 ?
The general solution for sin(x)=(-sqrt(3))/2 ,270<x<360 is x=300