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

The general solution for cos((-pi)/2+x/2)=0 is x=4pin+2pi,x=4pin+4pi

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cos((-pi)/2+x/2)=0

Solution

cos (\frac{- π}{2} + \frac{x}{2}) = 0

Solution

x = 4 πn + 2 π, x = 4 πn + 4 π

Degrees

x = 36 0^{\circ} + 72 0^{\circ} n, x = 72 0^{\circ} + 72 0^{\circ} n

Solution steps

cos (\frac{- π}{2} + \frac{x}{2}) = 0

General solutions for

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

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

Solve

\frac{- π}{2} + \frac{x}{2} = \frac{π}{2} + 2 πn : x = 4 πn + 2 π

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

Move

\frac{- π}{2}

to the right side

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

Subtract

\frac{- π}{2}

from both sides

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

Simplify

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

Simplify

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

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

Add similar elements:

\frac{- π}{2} - \frac{- π}{2} = 0

= \frac{x}{2}

Simplify

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

\frac{π}{2} + 2 πn - \frac{- π}{2}

Group like terms

= 2 πn + \frac{π}{2} - \frac{- π}{2}

Combine the fractions

\frac{π}{2} - \frac{- π}{2} : π

Apply rule

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

= \frac{π + π}{2}

Add similar elements:

π + π = 2 π

= \frac{2 π}{2}

Divide the numbers:

\frac{2}{2} = 1

= π

= 2 πn + π

\frac{x}{2} = 2 πn + π

\frac{x}{2} = 2 πn + π

\frac{x}{2} = 2 πn + π

Multiply both sides by

2

\frac{x}{2} = 2 πn + π

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot 2 πn + 2 π

Simplify

x = 4 πn + 2 π

x = 4 πn + 2 π

Solve

\frac{- π}{2} + \frac{x}{2} = \frac{3 π}{2} + 2 πn : x = 4 πn + 4 π

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

Move

\frac{- π}{2}

to the right side

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

Subtract

\frac{- π}{2}

from both sides

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

Simplify

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

Simplify

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

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

Add similar elements:

\frac{- π}{2} - \frac{- π}{2} = 0

= \frac{x}{2}

Simplify

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

\frac{3 π}{2} + 2 πn - \frac{- π}{2}

Group like terms

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

Combine the fractions

\frac{3 π}{2} - \frac{- π}{2} : 2 π

Apply rule

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

= \frac{3 π + π}{2}

Add similar elements:

3 π + π = 4 π

= \frac{4 π}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2 π

= 2 πn + 2 π

\frac{x}{2} = 2 πn + 2 π

\frac{x}{2} = 2 πn + 2 π

\frac{x}{2} = 2 πn + 2 π

Multiply both sides by

2

\frac{x}{2} = 2 πn + 2 π

Multiply both sides by

2

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

Simplify

x = 4 πn + 4 π

x = 4 πn + 4 π

x = 4 πn + 2 π, x = 4 πn + 4 π

Popular Examples

cos(x)=-0.175

cos (x) = - 0.175

sec^2(x)=2tan^2(x)

sec^{2} (x) = 2 tan^{2} (x)

(sin(x))/(cos(x))-5+(4cos(x))/(sin(x))=0

\frac{sin ( x )}{cos ( x )} - 5 + \frac{4 cos ( x )}{sin ( x )} = 0

solvefor x,y=sin(3.2x)solve for

x, y = sin (3.2 x)

sin(x)=0.37,pi<x< pi/2

sin (x) = 0.37, π < x < \frac{π}{2}

Frequently Asked Questions (FAQ)

What is the general solution for cos((-pi)/2+x/2)=0 ?
The general solution for cos((-pi)/2+x/2)=0 is x=4pin+2pi,x=4pin+4pi