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

The general solution for cos(pix)=1 is x=2n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

cos(pix)=1

cos (π x) = 1

x = 2 n

Degrees

x = 0^{\circ} + 114.59155 \dots^{\circ} n

Solution steps

cos (π x) = 1

General solutions for

cos (π x) = 1

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}

π x = 0 + 2 πn

π x = 0 + 2 πn

Solve

π x = 0 + 2 πn : x = 2 n

π x = 0 + 2 πn

0 + 2 πn = 2 πn

π x = 2 πn

Divide both sides by

π

π x = 2 πn

Divide both sides by

π

\frac{π x}{π} = \frac{2 πn}{π}

Simplify

x = 2 n

x = 2 n

x = 2 n

What is the general solution for cos(pix)=1 ?
The general solution for cos(pix)=1 is x=2n