What is the general solution for cos(-(pi/6)-2x)=1 ?

The general solution for cos(-(pi/6)-2x)=1 is x=-pin-pi/(12)

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cos(-(pi/6)-2x)=1

Solution

cos (- (\frac{π}{6}) - 2 x) = 1

Solution

x = - πn - \frac{π}{12}

Degrees

x = - 1 5^{\circ} - 18 0^{\circ} n

Solution steps

cos (- (\frac{π}{6}) - 2 x) = 1

General solutions for

cos (- \frac{π}{6} - 2 x) = 1

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

- \frac{π}{6} - 2 x = 0 + 2 πn

- \frac{π}{6} - 2 x = 0 + 2 πn

Solve

- \frac{π}{6} - 2 x = 0 + 2 πn : x = - πn - \frac{π}{12}

- \frac{π}{6} - 2 x = 0 + 2 πn

0 + 2 πn = 2 πn

- \frac{π}{6} - 2 x = 2 πn

Move

\frac{π}{6}

to the right side

- \frac{π}{6} - 2 x = 2 πn

Add

\frac{π}{6}

to both sides

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

Simplify

- 2 x = 2 πn + \frac{π}{6}

- 2 x = 2 πn + \frac{π}{6}

Divide both sides by

- 2

- 2 x = 2 πn + \frac{π}{6}

Divide both sides by

- 2

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

Simplify

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

Simplify

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

Apply the fraction rule:

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

= \frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{2 πn}{- 2} + \frac{\frac{π}{6}}{- 2} : - πn - \frac{π}{12}

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

\frac{2 πn}{- 2} = - πn

\frac{2 πn}{- 2}

Apply the fraction rule:

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

= - \frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= - πn

= - πn + \frac{\frac{π}{6}}{- 2}

\frac{\frac{π}{6}}{- 2} = - \frac{π}{12}

\frac{\frac{π}{6}}{- 2}

Apply the fraction rule:

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

= - \frac{\frac{π}{6}}{2}

Apply the fraction rule:

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

\frac{\frac{π}{6}}{2} = \frac{π}{6 \cdot 2}

= - \frac{π}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= - \frac{π}{12}

= - πn - \frac{π}{12}

x = - πn - \frac{π}{12}

x = - πn - \frac{π}{12}

x = - πn - \frac{π}{12}

x = - πn - \frac{π}{12}

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Frequently Asked Questions (FAQ)

What is the general solution for cos(-(pi/6)-2x)=1 ?
The general solution for cos(-(pi/6)-2x)=1 is x=-pin-pi/(12)