What is the general solution for 1/2 sin(x)=-(sqrt(3))/4 ?

The general solution for 1/2 sin(x)=-(sqrt(3))/4 is x=(4pi)/3+2pin,x=(5pi)/3+2pin

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1/2 sin(x)=-(sqrt(3))/4

\frac{1}{2} sin (x) = - \frac{3}{4}

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

Degrees

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

Solution steps

\frac{1}{2} sin (x) = - \frac{3}{4}

Multiply both sides by

2

\frac{1}{2} sin (x) = - \frac{3}{4}

Multiply both sides by

2

2 \cdot \frac{1}{2} sin (x) = 2 (- \frac{3}{4})

Simplify

2 \cdot \frac{1}{2} sin (x) = 2 (- \frac{3}{4})

Simplify

2 \cdot \frac{1}{2} sin (x) : sin (x)

2 \cdot \frac{1}{2} sin (x)

Multiply fractions:

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

= \frac{1 \cdot 2}{2} sin (x)

Cancel the common factor:

2

= sin (x) \cdot 1

Multiply:

sin (x) \cdot 1 = sin (x)

= sin (x)

Simplify

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

2 (- \frac{3}{4})

Remove parentheses:

(- a) = - a

= - 2 \cdot \frac{3}{4}

Multiply fractions:

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

= - \frac{3 \cdot 2}{4}

Cancel the common factor:

2

= - \frac{3}{2}

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

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

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

General solutions for

sin (x) = - \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}

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

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

cos^{2} (x) + 3 cos (x) - 4 = 0

7 sin (x) = cos (x) - 3

sin (a) = \frac{3}{4}

sin (7 x) + sin (x) = 0, 0 \leq x \leq 2 π

t, - 2 sin (t) + 2 cos (2 t) = 0

What is the general solution for 1/2 sin(x)=-(sqrt(3))/4 ?
The general solution for 1/2 sin(x)=-(sqrt(3))/4 is x=(4pi)/3+2pin,x=(5pi)/3+2pin