What is the general solution for cos(pi/2-x)=0 ?

The general solution for cos(pi/2-x)=0 is x=-2pin,x=-2pin-pi

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cos(pi/2-x)=0

Solution

cos (\frac{π}{2} - x) = 0

Solution

x = - 2 πn, x = - 2 πn - π

Degrees

x = 0^{\circ} - 36 0^{\circ} n, x = - 18 0^{\circ} - 36 0^{\circ} n

Solution steps

cos (\frac{π}{2} - x) = 0

General solutions for

cos (\frac{π}{2} - x) = 0

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

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

Solve

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

\frac{π}{2} - x = \frac{π}{2} + 2 πn

Subtract

\frac{π}{2}

from both sides

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

Simplify

- x = 2 πn

Divide both sides by

- 1

- x = 2 πn

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{2 πn}{- 1}

Simplify

x = - 2 πn

x = - 2 πn

Solve

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

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

Move

\frac{π}{2}

to the right side

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

Subtract

\frac{π}{2}

from both sides

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

Simplify

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

Simplify

\frac{π}{2} - x - \frac{π}{2} : - x

\frac{π}{2} - x - \frac{π}{2}

Add similar elements:

\frac{π}{2} - \frac{π}{2} = 0

= - x

Simplify

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

\frac{3 π}{2} + 2 πn - \frac{π}{2}

Group like terms

= 2 πn - \frac{π}{2} + \frac{3 π}{2}

Combine the fractions

- \frac{π}{2} + \frac{3 π}{2} : π

Apply rule

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

= \frac{- π + 3 π}{2}

Add similar elements:

- π + 3 π = 2 π

= \frac{2 π}{2}

Divide the numbers:

\frac{2}{2} = 1

= π

= 2 πn + π

- x = 2 πn + π

- x = 2 πn + π

- x = 2 πn + π

Divide both sides by

- 1

- x = 2 πn + π

Divide both sides by

- 1

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

Simplify

\frac{- x}{- 1} = \frac{2 πn}{- 1} + \frac{π}{- 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{π}{- 1} : - 2 πn - π

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

\frac{π}{- 1} = - π

\frac{π}{- 1}

Apply the fraction rule:

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

= - \frac{π}{1}

Apply rule

\frac{a}{1} = a

= - π

= - 2 πn - π

x = - 2 πn - π

x = - 2 πn - π

x = - 2 πn - π

x = - 2 πn, x = - 2 πn - π

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Frequently Asked Questions (FAQ)

What is the general solution for cos(pi/2-x)=0 ?
The general solution for cos(pi/2-x)=0 is x=-2pin,x=-2pin-pi