What is the general solution for cos((pix)/4)= 1/2 ?

The general solution for cos((pix)/4)= 1/2 is x= 4/3+8n,x= 20/3+8n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos((pix)/4)= 1/2

Solution

cos (\frac{π x}{4}) = \frac{1}{2}

Solution

x = \frac{4}{3} + 8 n, x = \frac{20}{3} + 8 n

Degrees

x = 76.39437 \dots^{\circ} + 458.36623 \dots^{\circ} n, x = 381.97186 \dots^{\circ} + 458.36623 \dots^{\circ} n

Solution steps

cos (\frac{π x}{4}) = \frac{1}{2}

General solutions for

cos (\frac{π x}{4}) = \frac{1}{2}

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 x}{4} = \frac{π}{3} + 2 πn, \frac{π x}{4} = \frac{5 π}{3} + 2 πn

\frac{π x}{4} = \frac{π}{3} + 2 πn, \frac{π x}{4} = \frac{5 π}{3} + 2 πn

Solve

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

\frac{π x}{4} = \frac{π}{3} + 2 πn

Multiply both sides by

4

\frac{π x}{4} = \frac{π}{3} + 2 πn

Multiply both sides by

4

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

Simplify

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

Simplify

\frac{4 π x}{4} : π x

\frac{4 π x}{4}

Divide the numbers:

\frac{4}{4} = 1

= π x

Simplify

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

4 \cdot \frac{π}{3} + 4 \cdot 2 πn

Multiply

4 \cdot \frac{π}{3} : \frac{4 π}{3}

4 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 4}{3}

= \frac{4 π}{3} + 4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= \frac{4 π}{3} + 8 πn

π x = \frac{4 π}{3} + 8 πn

π x = \frac{4 π}{3} + 8 πn

π x = \frac{4 π}{3} + 8 πn

Divide both sides by

π

π x = \frac{4 π}{3} + 8 πn

Divide both sides by

π

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

Simplify

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

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{\frac{4 π}{3}}{π} + \frac{8 πn}{π} : \frac{4}{3} + 8 n

\frac{\frac{4 π}{3}}{π} + \frac{8 πn}{π}

\frac{\frac{4 π}{3}}{π} = \frac{4}{3}

\frac{\frac{4 π}{3}}{π}

Apply the fraction rule:

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

= \frac{4 π}{3 π}

Cancel the common factor:

π

= \frac{4}{3}

\frac{8 πn}{π} = 8 n

\frac{8 πn}{π}

Cancel the common factor:

π

= 8 n

= \frac{4}{3} + 8 n

x = \frac{4}{3} + 8 n

x = \frac{4}{3} + 8 n

x = \frac{4}{3} + 8 n

Solve

\frac{π x}{4} = \frac{5 π}{3} + 2 πn : x = \frac{20}{3} + 8 n

\frac{π x}{4} = \frac{5 π}{3} + 2 πn

Multiply both sides by

4

\frac{π x}{4} = \frac{5 π}{3} + 2 πn

Multiply both sides by

4

\frac{4 π x}{4} = 4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

Simplify

\frac{4 π x}{4} = 4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

Simplify

\frac{4 π x}{4} : π x

\frac{4 π x}{4}

Divide the numbers:

\frac{4}{4} = 1

= π x

Simplify

4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn : \frac{20 π}{3} + 8 πn

4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

4 \cdot \frac{5 π}{3} = \frac{20 π}{3}

4 \cdot \frac{5 π}{3}

Multiply fractions:

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

= \frac{5 π 4}{3}

Multiply the numbers:

5 \cdot 4 = 20

= \frac{20 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= \frac{20 π}{3} + 8 πn

π x = \frac{20 π}{3} + 8 πn

π x = \frac{20 π}{3} + 8 πn

π x = \frac{20 π}{3} + 8 πn

Divide both sides by

π

π x = \frac{20 π}{3} + 8 πn

Divide both sides by

π

\frac{π x}{π} = \frac{\frac{20 π}{3}}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} = \frac{\frac{20 π}{3}}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{\frac{20 π}{3}}{π} + \frac{8 πn}{π} : \frac{20}{3} + 8 n

\frac{\frac{20 π}{3}}{π} + \frac{8 πn}{π}

\frac{\frac{20 π}{3}}{π} = \frac{20}{3}

\frac{\frac{20 π}{3}}{π}

Apply the fraction rule:

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

= \frac{20 π}{3 π}

Cancel the common factor:

π

= \frac{20}{3}

\frac{8 πn}{π} = 8 n

\frac{8 πn}{π}

Cancel the common factor:

π

= 8 n

= \frac{20}{3} + 8 n

x = \frac{20}{3} + 8 n

x = \frac{20}{3} + 8 n

x = \frac{20}{3} + 8 n

x = \frac{4}{3} + 8 n, x = \frac{20}{3} + 8 n

Graph

Popular Examples

solvefor x,cos(2x)=1 solve for

x, cos (2 x) = 1

5cos(x)cot(x)=1

5 cos (x) cot (x) = 1

2cos^2(x)=-1

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

-0.5=cos(3x)

- 0.5 = cos (3 x)

sin(3x)=-0.5

sin (3 x) = - 0.5

Frequently Asked Questions (FAQ)

What is the general solution for cos((pix)/4)= 1/2 ?
The general solution for cos((pix)/4)= 1/2 is x= 4/3+8n,x= 20/3+8n