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

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

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-1=cos(3x)

- 1 = cos (3 x)

x = \frac{π}{3} + \frac{2 πn}{3}

Degrees

x = 6 0^{\circ} + 12 0^{\circ} n

Solution steps

- 1 = cos (3 x)

Switch sides

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 = π + 2 πn

3 x = π + 2 πn

Solve

3 x = π + 2 πn : x = \frac{π}{3} + \frac{2 πn}{3}

3 x = π + 2 πn

Divide both sides by

3

3 x = π + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{π}{3} + \frac{2 πn}{3}

Simplify

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

2 cos^{2} (θ) + 3 sin (θ) - 3 = 0

sec (θ) = \frac{4}{5}

- 2 = 22 cos (θ)

cos^{2} (2 x) = 1

- 4 cos^{2} (θ) = - 1

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