What is the periodicity of f(x)=sin^4(x)-sin^2(x) ?

The periodicity of f(x)=sin^4(x)-sin^2(x) is pi

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periodicity of f(x)=sin^4(x)-sin^2(x)

periodicity

f (x) = sin^{4} (x) - sin^{2} (x)

π

Solution steps

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

sin^{4} (x), sin^{2} (x)

Periodicity of

sin^{4} (x) : π

Periodicity of

sin^{2} (x) : π

Combine periods:

π, π

= π

f (x) = - x^{2} - 10 x + 16

f (x) = \frac{4 x}{x + 1}

f (x) = x^{2} - 6 x - 10

f (x) = - (x + 2) (x - 6)

f (x) = x, - π < x < π

What is the periodicity of f(x)=sin^4(x)-sin^2(x) ?
The periodicity of f(x)=sin^4(x)-sin^2(x) is pi