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

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

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cos(((2x-pi))/4)=1

cos (\frac{( 2 x - π )}{4}) = 1

x = 4 πn + \frac{π}{2}

Degrees

x = 9 0^{\circ} + 72 0^{\circ} n

Solution steps

cos (\frac{( 2 x - π )}{4}) = 1

General solutions for

cos (\frac{2 x - 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}

\frac{2 x - π}{4} = 0 + 2 πn

\frac{2 x - π}{4} = 0 + 2 πn

Solve

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

\frac{2 x - π}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{2 x - π}{4} = 2 πn

Multiply both sides by

4

\frac{2 x - π}{4} = 2 πn

Multiply both sides by

4

\frac{4 ( 2 x - π )}{4} = 4 \cdot 2 πn

Simplify

2 x - π = 8 πn

2 x - π = 8 πn

Move

π

to the right side

2 x - π = 8 πn

Add

π

to both sides

2 x - π + π = 8 πn + π

Simplify

2 x = 8 πn + π

2 x = 8 πn + π

Divide both sides by

2

2 x = 8 πn + π

Divide both sides by

2

\frac{2 x}{2} = \frac{8 πn}{2} + \frac{π}{2}

Simplify

x = 4 πn + \frac{π}{2}

x = 4 πn + \frac{π}{2}

x = 4 πn + \frac{π}{2}

\frac{5}{6} sin (10 x - 0.927) = 5

3 sin (t) = 1 + sin (t)

sin^{2} (t) sin (t) = 0

cos (x) = \frac{100}{130}

sec^{2} (θ) - 1 = 0, 0 \leq θ \leq 2 π

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