What is the general solution for cos(x+pi/4)=1 ?

The general solution for cos(x+pi/4)=1 is x=2pin-pi/4

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cos(x+pi/4)=1

cos (x + \frac{π}{4}) = 1

x = 2 πn - \frac{π}{4}

Degrees

x = - 4 5^{\circ} + 36 0^{\circ} n

Solution steps

cos (x + \frac{π}{4}) = 1

General solutions for

cos (x + \frac{π}{4}) = 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 + \frac{π}{4} = 0 + 2 πn

x + \frac{π}{4} = 0 + 2 πn

Solve

x + \frac{π}{4} = 0 + 2 πn : x = 2 πn - \frac{π}{4}

x + \frac{π}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

x + \frac{π}{4} = 2 πn

Move

\frac{π}{4}

to the right side

x + \frac{π}{4} = 2 πn

Subtract

\frac{π}{4}

from both sides

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

Simplify

x = 2 πn - \frac{π}{4}

x = 2 πn - \frac{π}{4}

x = 2 πn - \frac{π}{4}

arctan (x) = - 180

9 + sin^{2} (x) = 10

tan^{2} (3 x) = 1

3 + 3 sin (θ) = 0

cos (2 x) = \frac{( 8 k - 7 )}{7}

What is the general solution for cos(x+pi/4)=1 ?
The general solution for cos(x+pi/4)=1 is x=2pin-pi/4