What is the FUNCTION_MANY#periodicity of f(x)=2sin^4(2x)-3sin^3(4x) ?

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FUNCTION_MANY#periodicity of f(x)=2sin^4(2x)-3sin^3(4x)

periodicity

f (x) = 2 sin^{4} (2 x) - 3 sin^{3} (4 x)

π

Decimal

3.14159 \dots

Solution steps

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

2 sin^{4} (2 x), 3 sin^{3} (4 x)

Periodicity of

2 sin^{4} (2 x) : \frac{π}{2}

Periodicity of

3 sin^{3} (4 x) : \frac{π}{2}

Combine periods:

\frac{π}{2}, \frac{π}{2}

= π

What is the FUNCTION_MANY#periodicity of f(x)=2sin^4(2x)-3sin^3(4x) ?
The FUNCTION_MANY#periodicity of f(x)=2sin^4(2x)-3sin^3(4x) is pi