What is the general solution for cos(1/2 x)=0 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(1/2 x)=0

Solution

cos (\frac{1}{2} x) = 0

Solution

x = π + 4 πn, x = 3 π + 4 πn

Degrees

x = 18 0^{\circ} + 72 0^{\circ} n, x = 54 0^{\circ} + 72 0^{\circ} n

Solution steps

cos (\frac{1}{2} x) = 0

General solutions for

cos (\frac{1}{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{1}{2} x = \frac{π}{2} + 2 πn, \frac{1}{2} x = \frac{3 π}{2} + 2 πn

\frac{1}{2} x = \frac{π}{2} + 2 πn, \frac{1}{2} x = \frac{3 π}{2} + 2 πn

Solve

\frac{1}{2} x = \frac{π}{2} + 2 πn : x = π + 4 πn

\frac{1}{2} x = \frac{π}{2} + 2 πn

Multiply both sides by

2

\frac{1}{2} x = \frac{π}{2} + 2 πn

Multiply both sides by

2

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

Simplify

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

Simplify

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiply fractions:

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

= \frac{1 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 1

Multiply:

x \cdot 1 = x

= x

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

x = π + 4 πn

x = π + 4 πn

x = π + 4 πn

Solve

\frac{1}{2} x = \frac{3 π}{2} + 2 πn : x = 3 π + 4 πn

\frac{1}{2} x = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

\frac{1}{2} x = \frac{3 π}{2} + 2 πn

Multiply both sides by

2

2 \cdot \frac{1}{2} x = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{1}{2} x = 2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

Simplify

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

Multiply fractions:

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

= \frac{1 \cdot 2}{2} x

Cancel the common factor:

2

= x \cdot 1

Multiply:

x \cdot 1 = x

= x

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

x = 3 π + 4 πn

x = 3 π + 4 πn

x = 3 π + 4 πn

x = π + 4 πn, x = 3 π + 4 πn

Popular Examples

(4cos(θ)-1)/(tan(θ))=2sin(θ)

\frac{4 cos ( θ ) - 1}{tan ( θ )} = 2 sin (θ)

-2sin^2(x)-cos(x)=-1,0<= x<360

- 2 sin^{2} (x) - cos (x) = - 1, 0^{\circ} \leq x < 36 0^{\circ}

cos^2(θ)-3cos(θ)+2=sin^2(θ)

cos^{2} (θ) - 3 cos (θ) + 2 = sin^{2} (θ)

sin(x)-cos^2(x)-1=0

sin (x) - cos^{2} (x) - 1 = 0

2+2sin(θ)=-4sin(θ)

2 + 2 sin (θ) = - 4 sin (θ)

Frequently Asked Questions (FAQ)

What is the general solution for cos(1/2 x)=0 ?
The general solution for cos(1/2 x)=0 is x=pi+4pin,x=3pi+4pin