What is the periodicity of f(x)=cos(6x)-3sin(3x)+1 ?

The periodicity of f(x)=cos(6x)-3sin(3x)+1 is 2pi

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periodicity of f(x)=cos(6x)-3sin(3x)+1

periodicity

f (x) = cos (6 x) - 3 sin (3 x) + 1

2 π

Solution steps

Periodicity of

f (x) + c =

Periodicity of

f (x)

c = 1

= periodicity of cos (6 x) - 3 sin (3 x)

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

cos (6 x), 3 sin (3 x)

Periodicity of

cos (6 x) : \frac{π}{3}

Periodicity of

3 sin (3 x) : \frac{2 π}{3}

Combine periods:

\frac{π}{3}, \frac{2 π}{3}

= 2 π

f (x) = x^{3} + 4 x^{2} + 2

f (x) = \frac{x ^{2} + 2 x}{1} + \frac{3 x - x ^{2}}{2 x}

y = 4 x^{2} + 24 x

y = \frac{3 x ^{2} + 2 x + 4}{x ^{2} - 2 x + 1}

What is the periodicity of f(x)=cos(6x)-3sin(3x)+1 ?
The periodicity of f(x)=cos(6x)-3sin(3x)+1 is 2pi