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

The general solution for cos(pi/2 x)=0 is x=1+4n,x=3+4n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(pi/2 x)=0

Solution

cos (\frac{π}{2} x) = 0

Solution

x = 1 + 4 n, x = 3 + 4 n

Degrees

x = 57.29577 \dots^{\circ} + 229.18311 \dots^{\circ} n, x = 171.88733 \dots^{\circ} + 229.18311 \dots^{\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 = 1 + 4 n

\frac{π}{2} x = \frac{π}{2} + 2 πn

Multiply both sides by

2

\frac{π}{2} x = \frac{π}{2} + 2 πn

Multiply both sides by

2

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

Simplify

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

Simplify

2 \cdot \frac{π}{2} x : π x

2 \cdot \frac{π}{2} x

Multiply fractions:

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

= \frac{2 π}{2} x

Cancel the common factor:

2

= x π

Simplify

2 \cdot \frac{π}{2} + 2 \cdot 2 πn : π + 4 πn

2 \cdot \frac{π}{2} + 2 \cdot 2 πn

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 2}{2}

Cancel the common factor:

2

= π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= π + 4 πn

π x = π + 4 πn

π x = π + 4 πn

π x = π + 4 πn

Divide both sides by

π

π x = π + 4 πn

Divide both sides by

π

\frac{π x}{π} = \frac{π}{π} + \frac{4 πn}{π}

Simplify

\frac{π x}{π} = \frac{π}{π} + \frac{4 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{π}{π} + \frac{4 πn}{π} : 1 + 4 n

\frac{π}{π} + \frac{4 πn}{π}

Apply rule

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{4 πn}{π}

Cancel

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Cancel the common factor:

π

= 4 n

= 1 + 4 n

x = 1 + 4 n

x = 1 + 4 n

x = 1 + 4 n

Solve

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

\frac{π}{2} x = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

\frac{π}{2} x = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

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

Simplify

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

Simplify

2 \cdot \frac{π}{2} x : π x

2 \cdot \frac{π}{2} x

Multiply fractions:

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

= \frac{2 π}{2} x

Cancel the common factor:

2

= x π

Simplify

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn : 3 π + 4 πn

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

2 \cdot \frac{3 π}{2} = 3 π

2 \cdot \frac{3 π}{2}

Multiply fractions:

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

= \frac{3 π 2}{2}

Cancel the common factor:

2

= 3 π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 4 πn

= 3 π + 4 πn

π x = 3 π + 4 πn

π x = 3 π + 4 πn

π x = 3 π + 4 πn

Divide both sides by

π

π x = 3 π + 4 πn

Divide both sides by

π

\frac{π x}{π} = \frac{3 π}{π} + \frac{4 πn}{π}

Simplify

\frac{π x}{π} = \frac{3 π}{π} + \frac{4 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{3 π}{π} + \frac{4 πn}{π} : 3 + 4 n

\frac{3 π}{π} + \frac{4 πn}{π}

Cancel

\frac{3 π}{π} : 3

\frac{3 π}{π}

Cancel the common factor:

π

= 3

= 3 + \frac{4 πn}{π}

Cancel

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

Cancel the common factor:

π

= 4 n

= 3 + 4 n

x = 3 + 4 n

x = 3 + 4 n

x = 3 + 4 n

x = 1 + 4 n, x = 3 + 4 n

Popular Examples

sin(3θ)-sin(6θ)=0

sin (3 θ) - sin (6 θ) = 0

sec(x)=-2/(sqrt(3))

sec (x) = - \frac{2}{3}

csc(2x)=-2

csc (2 x) = - 2

tan(θ)= 13/9

tan (θ) = \frac{13}{9}

sin(x/2)=(-sqrt(3))/2

sin (\frac{x}{2}) = \frac{- 3}{2}

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=1+4n,x=3+4n