What is the general solution for cos(3x)=1 ?

The general solution for cos(3x)=1 is x=(2pin)/3

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cos(3x)=1

cos (3 x) = 1

x = \frac{2 πn}{3}

Degrees

x = 0^{\circ} + 12 0^{\circ} n

Solution steps

cos (3 x) = 1

General solutions for

cos (3 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}

3 x = 0 + 2 πn

3 x = 0 + 2 πn

Solve

3 x = 0 + 2 πn : x = \frac{2 πn}{3}

3 x = 0 + 2 πn

0 + 2 πn = 2 πn

3 x = 2 πn

Divide both sides by

3

3 x = 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{2 πn}{3}

Simplify

x = \frac{2 πn}{3}

x = \frac{2 πn}{3}

x = \frac{2 πn}{3}

3 sin^{2} (x) = cos^{2} (x)

sec (arcsin (- \frac{2}{2}))

2 sin^{2} (x) - sin (x) - 3 = 0

sec (21 0^{\circ})

tan (x) + cot (x) = sec (x) csc (x)

What is the general solution for cos(3x)=1 ?
The general solution for cos(3x)=1 is x=(2pin)/3