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Popular >

sin(pi-3x)= 1/2

Solution

sin (π - 3 x) = \frac{1}{2}

Solution

x = \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}, x = \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

Degrees

x = 5 0^{\circ} - 12 0^{\circ} n, x = 1 0^{\circ} - 12 0^{\circ} n

Solution steps

sin (π - 3 x) = \frac{1}{2}

General solutions for

sin (π - 3 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}

π - 3 x = \frac{π}{6} + 2 πn, π - 3 x = \frac{5 π}{6} + 2 πn

π - 3 x = \frac{π}{6} + 2 πn, π - 3 x = \frac{5 π}{6} + 2 πn

Solve

π - 3 x = \frac{π}{6} + 2 πn : x = \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}

π - 3 x = \frac{π}{6} + 2 πn

Move

π

to the right side

π - 3 x = \frac{π}{6} + 2 πn

Subtract

π

from both sides

π - 3 x - π = \frac{π}{6} + 2 πn - π

Simplify

- 3 x = \frac{π}{6} + 2 πn - π

- 3 x = \frac{π}{6} + 2 πn - π

Divide both sides by

- 3

- 3 x = \frac{π}{6} + 2 πn - π

Divide both sides by

- 3

\frac{- 3 x}{- 3} = \frac{\frac{π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3}

Simplify

\frac{- 3 x}{- 3} = \frac{\frac{π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3}

Simplify

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Apply the fraction rule:

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

= \frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3} : \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}

\frac{\frac{π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3}

Group like terms

= - \frac{π}{- 3} + \frac{2 πn}{- 3} + \frac{\frac{π}{6}}{- 3}

Refine

= \frac{π}{3} - \frac{2 πn}{3} + \frac{\frac{π}{6}}{- 3}

\frac{\frac{π}{6}}{- 3} = - \frac{π}{18}

\frac{\frac{π}{6}}{- 3}

Apply the fraction rule:

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

= - \frac{\frac{π}{6}}{3}

Apply the fraction rule:

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

\frac{\frac{π}{6}}{3} = \frac{π}{6 \cdot 3}

= - \frac{π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= - \frac{π}{18}

= \frac{π}{3} - \frac{2 πn}{3} - \frac{π}{18}

Group like terms

= \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}

x = \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}

x = \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}

x = \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}

Solve

π - 3 x = \frac{5 π}{6} + 2 πn : x = \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

π - 3 x = \frac{5 π}{6} + 2 πn

Move

π

to the right side

π - 3 x = \frac{5 π}{6} + 2 πn

Subtract

π

from both sides

π - 3 x - π = \frac{5 π}{6} + 2 πn - π

Simplify

- 3 x = \frac{5 π}{6} + 2 πn - π

- 3 x = \frac{5 π}{6} + 2 πn - π

Divide both sides by

- 3

- 3 x = \frac{5 π}{6} + 2 πn - π

Divide both sides by

- 3

\frac{- 3 x}{- 3} = \frac{\frac{5 π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3}

Simplify

\frac{- 3 x}{- 3} = \frac{\frac{5 π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3}

Simplify

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Apply the fraction rule:

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

= \frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3} : \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{- 3} + \frac{2 πn}{- 3} - \frac{π}{- 3}

Group like terms

= - \frac{π}{- 3} + \frac{2 πn}{- 3} + \frac{\frac{5 π}{6}}{- 3}

Refine

= \frac{π}{3} - \frac{2 πn}{3} + \frac{\frac{5 π}{6}}{- 3}

\frac{\frac{5 π}{6}}{- 3} = - \frac{5 π}{18}

\frac{\frac{5 π}{6}}{- 3}

Apply the fraction rule:

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

= - \frac{\frac{5 π}{6}}{3}

Apply the fraction rule:

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

\frac{\frac{5 π}{6}}{3} = \frac{5 π}{6 \cdot 3}

= - \frac{5 π}{6 \cdot 3}

Multiply the numbers:

6 \cdot 3 = 18

= - \frac{5 π}{18}

= \frac{π}{3} - \frac{2 πn}{3} - \frac{5 π}{18}

Group like terms

= \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

x = \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

x = \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

x = \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

x = \frac{π}{3} - \frac{π}{18} - \frac{2 πn}{3}, x = \frac{π}{3} - \frac{5 π}{18} - \frac{2 πn}{3}

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