What is the periodicity of f(x)=sin(2x)-cos(5x) ?

The periodicity of f(x)=sin(2x)-cos(5x) is 2pi

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periodicity of f(x)=sin(2x)-cos(5x)

periodicity

f (x) = sin (2 x) - cos (5 x)

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 (2 x), cos (5 x)

Periodicity of

sin (2 x) : π

Periodicity of

cos (5 x) : \frac{2 π}{5}

Combine periods:

π, \frac{2 π}{5}

= 2 π

What is the periodicity of f(x)=sin(2x)-cos(5x) ?
The periodicity of f(x)=sin(2x)-cos(5x) is 2pi