What is the general solution for sin(x)=(-4/3 sqrt(3))/(8/3 sqrt(3)) ?

The general solution for sin(x)=(-4/3 sqrt(3))/(8/3 sqrt(3)) is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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sin(x)=(-4/3 sqrt(3))/(8/3 sqrt(3))

sin (x) = \frac{- \frac{4}{3} 3}{\frac{8}{3} 3}

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

sin (x) = \frac{- \frac{4}{3} 3}{\frac{8}{3} 3}

Simplify

\frac{- \frac{4}{3} 3}{\frac{8}{3} 3} : - \frac{1}{2}

\frac{- \frac{4}{3} 3}{\frac{8}{3} 3}

Apply the fraction rule:

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

= - \frac{\frac{4}{3} 3}{\frac{8}{3} 3}

Multiply

\frac{4}{3} 3 : \frac{4}{3}

\frac{4}{3} 3

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{4 \cdot 3 ^{\frac{1}{2}}}{3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{4}{3 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{4}{3 ^{\frac{1}{2}}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= \frac{4}{3}

= - \frac{\frac{4}{3}}{3 \frac{8}{3}}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= - \frac{4}{3 3 \frac{8}{3}}

3 \frac{8}{3} 3 = 3 \cdot \frac{8}{3}

3 \frac{8}{3} 3

Apply radical rule:

a a = a

33 = 3

= 3 \cdot \frac{8}{3}

= - \frac{4}{3 \cdot \frac{8}{3}}

Multiply

\frac{8}{3} \cdot 3 : 8

\frac{8}{3} \cdot 3

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8 \cdot 3}{3}

Cancel the common factor:

3

= 8

= - \frac{4}{8}

Cancel the common factor:

4

= - \frac{1}{2}

General solutions for

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sec (a) = \frac{5}{4}

cot^{4} (x) - 9 = 0

0.5 \cdot sin (x) = 1 \cdot (645 \cdot 1 0^{- 9})

sin (2 x) = 2 cos (2 x)

5 tan^{2} (x) - 7 = 8

What is the general solution for sin(x)=(-4/3 sqrt(3))/(8/3 sqrt(3)) ?
The general solution for sin(x)=(-4/3 sqrt(3))/(8/3 sqrt(3)) is x=(7pi)/6+2pin,x=(11pi)/6+2pin