What is the general solution for solvefor x,cos(x-y)=1 ?

The general solution for solvefor x,cos(x-y)=1 is x=2pin+y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor x,cos(x-y)=1

solve for

x, cos (x - y) = 1

x = 2 πn + y

Solution steps

cos (x - y) = 1

General solutions for

cos (x - y) = 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}

x - y = 0 + 2 πn

x - y = 0 + 2 πn

Solve

x - y = 0 + 2 πn : x = 2 πn + y

x - y = 0 + 2 πn

0 + 2 πn = 2 πn

x - y = 2 πn

Move

y

to the right side

x - y = 2 πn

Add

y

to both sides

x - y + y = 2 πn + y

Simplify

x = 2 πn + y

x = 2 πn + y

x = 2 πn + y

x, cos (x - y) = 0

sin (a) + 1 = 2 1 - sin^{2} (a)

4 cos (x) - 3 = 0

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{1}{2}

8 sin (x) tan (x) + tan (x) = 0

What is the general solution for solvefor x,cos(x-y)=1 ?
The general solution for solvefor x,cos(x-y)=1 is x=2pin+y