What is the general solution for cos(x+pi)=1 ?

The general solution for cos(x+pi)=1 is x=2pin-pi

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cos(x+pi)=1

cos (x + π) = 1

x = 2 πn - π

Degrees

x = - 18 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (x + π) = 1

General solutions for

cos (x + π) = 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 + π = 0 + 2 πn

x + π = 0 + 2 πn

Solve

x + π = 0 + 2 πn : x = 2 πn - π

x + π = 0 + 2 πn

0 + 2 πn = 2 πn

x + π = 2 πn

Move

π

to the right side

x + π = 2 πn

Subtract

π

from both sides

x + π - π = 2 πn - π

Simplify

x = 2 πn - π

x = 2 πn - π

x = 2 πn - π

x, sin (4 x) = - 2 (sin (2 x))

(1 + cos (2 x)) sin (x) = 2 cos (x) sin (x)

sin (b) = \frac{2}{3}

8 tan (x) - 3 = 4

tan (θ) - 4 = 0

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