What is the general solution for cos(2θ)-cos(4θ)=0 ?

The general solution for cos(2θ)-cos(4θ)=0 is θ=(2pin)/3 ,θ= pi/3+(2pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(2θ)-cos(4θ)=0

cos (2 θ) - cos (4 θ) = 0

θ = \frac{2 πn}{3}, θ = \frac{π}{3} + \frac{2 πn}{3}

Solution steps

cos (2 θ) - cos (4 θ) = 0

Rewrite using trig identities

2 sin (3 θ) sin (θ) = 0

Solving each part separately

sin (3 θ) = 0 or sin (θ) = 0

sin (3 θ) = 0 : θ = \frac{2 πn}{3}, θ = \frac{π}{3} + \frac{2 πn}{3}

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

θ = \frac{2 πn}{3}, θ = \frac{π}{3} + \frac{2 πn}{3}, θ = 2 πn, θ = π + 2 πn

Merge Overlapping Intervals

θ = \frac{2 πn}{3}, θ = \frac{π}{3} + \frac{2 πn}{3}

tan (x) = 1.4

sin (θ) = 0.71

2 tan^{2} (x) - 3 tan (x) + 1 = 0

tan (x) = \frac{8}{6}

sin (4 x) + cos (4 x) = 0

What is the general solution for cos(2θ)-cos(4θ)=0 ?
The general solution for cos(2θ)-cos(4θ)=0 is θ=(2pin)/3 ,θ= pi/3+(2pin)/3