What is the general solution for cos(pi/3-x)=1 ?

The general solution for cos(pi/3-x)=1 is x=-2pin+pi/3

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cos(pi/3-x)=1

Solution

cos (\frac{π}{3} - x) = 1

Solution

x = - 2 πn + \frac{π}{3}

Degrees

x = 6 0^{\circ} - 36 0^{\circ} n

Solution steps

cos (\frac{π}{3} - x) = 1

General solutions for

cos (\frac{π}{3} - 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}{3} - x = 0 + 2 πn

\frac{π}{3} - x = 0 + 2 πn

Solve

\frac{π}{3} - x = 0 + 2 πn : x = - 2 πn + \frac{π}{3}

\frac{π}{3} - x = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{π}{3} - x = 2 πn

Move

\frac{π}{3}

to the right side

\frac{π}{3} - x = 2 πn

Subtract

\frac{π}{3}

from both sides

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

Simplify

- x = 2 πn - \frac{π}{3}

- x = 2 πn - \frac{π}{3}

Divide both sides by

- 1

- x = 2 πn - \frac{π}{3}

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{2 πn}{- 1} - \frac{\frac{π}{3}}{- 1}

Simplify

\frac{- x}{- 1} = \frac{2 πn}{- 1} - \frac{\frac{π}{3}}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{2 πn}{- 1} - \frac{\frac{π}{3}}{- 1} : - 2 πn + \frac{π}{3}

\frac{2 πn}{- 1} - \frac{\frac{π}{3}}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

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

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - 2 πn - \frac{\frac{π}{3}}{- 1}

\frac{\frac{π}{3}}{- 1} = - \frac{π}{3}

\frac{\frac{π}{3}}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{π}{3}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{π}{3}}{1} = \frac{π}{3}

= - \frac{π}{3}

= - 2 πn - (- \frac{π}{3})

Apply rule

- (- a) = a

= - 2 πn + \frac{π}{3}

x = - 2 πn + \frac{π}{3}

x = - 2 πn + \frac{π}{3}

x = - 2 πn + \frac{π}{3}

x = - 2 πn + \frac{π}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for cos(pi/3-x)=1 ?
The general solution for cos(pi/3-x)=1 is x=-2pin+pi/3