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

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

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cos(3A)=1

cos (3 A) = 1

A = \frac{2 πn}{3}

Degrees

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

Solution steps

cos (3 A) = 1

General solutions for

cos (3 A) = 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 A = 0 + 2 πn

3 A = 0 + 2 πn

Solve

3 A = 0 + 2 πn : A = \frac{2 πn}{3}

3 A = 0 + 2 πn

0 + 2 πn = 2 πn

3 A = 2 πn

Divide both sides by

3

3 A = 2 πn

Divide both sides by

3

\frac{3 A}{3} = \frac{2 πn}{3}

Simplify

A = \frac{2 πn}{3}

A = \frac{2 πn}{3}

A = \frac{2 πn}{3}

cos (θ) = (- 0.68159)

cot (x + \frac{5 π}{6}) = 3

θ, y = sin (θ)

sec^{2} (x) - 4 tan^{2} (x) = 0

6 cos^{2} (x) + cos (2 x) = 5

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