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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1=cos(3θ)

1 = cos (3 θ)

θ = \frac{2 πn}{3}

Degrees

θ = 0^{\circ} + 12 0^{\circ} n

Solution steps

1 = cos (3 θ)

Switch sides

cos (3 θ) = 1

General solutions for

cos (3 θ) = 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 θ = 0 + 2 πn

3 θ = 0 + 2 πn

Solve

3 θ = 0 + 2 πn : θ = \frac{2 πn}{3}

3 θ = 0 + 2 πn

0 + 2 πn = 2 πn

3 θ = 2 πn

Divide both sides by

3

3 θ = 2 πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{2 πn}{3}

Simplify

θ = \frac{2 πn}{3}

θ = \frac{2 πn}{3}

θ = \frac{2 πn}{3}

3 sin (2 x) + cos (x) = 0

sinh (a x) = 0

8 sin^{4} (x) - 3 sin^{2} (x) + \frac{1}{4} = 0

- 2 cot (θ) = - 1 - cot^{2} (θ)

- cos^{2} (x) - sin (x) - 1 = 0

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