What is the periodicity of f(x)=sin(3x)+sin(2(pi)x) ?

The periodicity of f(x)=sin(3x)+sin(2(pi)x) is 2pi

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periodicity of f(x)=sin(3x)+sin(2(pi)x)

periodicity

2 π

Decimal

6.28318 \dots

Solution steps

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

sin (3 x), sin (2 π x)

Periodicity of

sin (3 x) : \frac{2 π}{3}

Periodicity of

sin (2 π x) : 1

Combine periods:

\frac{2 π}{3}, 1

= 2 π

What is the periodicity of f(x)=sin(3x)+sin(2(pi)x) ?
The periodicity of f(x)=sin(3x)+sin(2(pi)x) is 2pi