What is the periodicity of f(θ)=cos(θ/2)-cos((3θ)/2) ?

The periodicity of f(θ)=cos(θ/2)-cos((3θ)/2) is 4pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

periodicity of f(θ)=cos(θ/2)-cos((3θ)/2)

periodicity

f (θ) = cos (\frac{θ}{2}) - cos (\frac{3 θ}{2})

4 π

Decimal

12.56637 \dots

Solution steps

The compound periodicity of the sum of periodic functions is the least common multiplier of the periods

cos (\frac{θ}{2}), cos (\frac{3 θ}{2})

Periodicity of

cos (\frac{θ}{2}) : 4 π

Periodicity of

cos (\frac{3 θ}{2}) : \frac{4 π}{3}

Combine periods:

4 π, \frac{4 π}{3}

= 4 π

f (x) = - x^{2} - 10

y = x + arctan (x)

f (x) = sin (e^{x^{2}})

f (θ) = cos (θ) - 1

f (x) = \frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}}

What is the periodicity of f(θ)=cos(θ/2)-cos((3θ)/2) ?
The periodicity of f(θ)=cos(θ/2)-cos((3θ)/2) is 4pi