What is the general solution for cos(x/4)=0 ?

The general solution for cos(x/4)=0 is x=2pi+8pin,x=6pi+8pin

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Popular >

cos(x/4)=0

Solution

cos (\frac{x}{4}) = 0

Solution

x = 2 π + 8 πn, x = 6 π + 8 πn

Degrees

x = 36 0^{\circ} + 144 0^{\circ} n, x = 108 0^{\circ} + 144 0^{\circ} n

Solution steps

cos (\frac{x}{4}) = 0

General solutions for

cos (\frac{x}{4}) = 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{x}{4} = \frac{π}{2} + 2 πn, \frac{x}{4} = \frac{3 π}{2} + 2 πn

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

Solve

\frac{x}{4} = \frac{π}{2} + 2 πn : x = 2 π + 8 πn

\frac{x}{4} = \frac{π}{2} + 2 πn

Multiply both sides by

4

\frac{x}{4} = \frac{π}{2} + 2 πn

Multiply both sides by

4

\frac{4 x}{4} = 4 \cdot \frac{π}{2} + 4 \cdot 2 πn

Simplify

\frac{4 x}{4} = 4 \cdot \frac{π}{2} + 4 \cdot 2 πn

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

4 \cdot \frac{π}{2} + 4 \cdot 2 πn : 2 π + 8 πn

4 \cdot \frac{π}{2} + 4 \cdot 2 πn

4 \cdot \frac{π}{2} = 2 π

4 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= 2 π + 8 πn

x = 2 π + 8 πn

x = 2 π + 8 πn

x = 2 π + 8 πn

Solve

\frac{x}{4} = \frac{3 π}{2} + 2 πn : x = 6 π + 8 πn

\frac{x}{4} = \frac{3 π}{2} + 2 πn

Multiply both sides by

4

\frac{x}{4} = \frac{3 π}{2} + 2 πn

Multiply both sides by

4

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

Simplify

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

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn : 6 π + 8 πn

4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

4 \cdot \frac{3 π}{2} = 6 π

4 \cdot \frac{3 π}{2}

Multiply fractions:

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

= \frac{3 π 4}{2}

Multiply the numbers:

3 \cdot 4 = 12

= \frac{12 π}{2}

Divide the numbers:

\frac{12}{2} = 6

= 6 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= 6 π + 8 πn

x = 6 π + 8 πn

x = 6 π + 8 πn

x = 6 π + 8 πn

x = 2 π + 8 πn, x = 6 π + 8 πn

Popular Examples

cos(θ)=0.92

cos (θ) = 0.92

sqrt(2)sin(2x)=1

2 sin (2 x) = 1

2cos(x)=sqrt(2)

2 cos (x) = 2

sin(θ)-1=0

sin (θ) - 1 = 0

sin(2θ)=1

sin (2 θ) = 1

Frequently Asked Questions (FAQ)

What is the general solution for cos(x/4)=0 ?
The general solution for cos(x/4)=0 is x=2pi+8pin,x=6pi+8pin