What is the general solution for sin(a)=(-sqrt(3))/2 ?

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

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sin(a)=(-sqrt(3))/2

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

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

Degrees

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

Solution steps

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

Apply the fraction rule:

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

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

General solutions for

sin (a) = - \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}

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

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

sin (x) = 467

csc (x) = \frac{5}{3}

sin (B) = \frac{( 240.68 \cdot sin ( 21.1 6 ^{\circ} ) )}{207.91}

2 sin (2 x + \frac{π}{4}) = - 1, - 2 π \leq x \leq 2 π

sin (φ) - cos (φ) = sin (φ) tan (φ)

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