What is the periodicity of f(x)=cos(4/pi t+30)-sin(4pit+30) ?

The periodicity of f(x)=cos(4/pi t+30)-sin(4pit+30) is pi^2

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periodicity of f(x)=cos(4/pi t+30)-sin(4pit+30)

periodicity

π^{2}

Decimal

9.86960 \dots

Solution steps

Convert

30

degrees to radians:

\frac{π}{6}

= cos (\frac{4}{π} t + \frac{π}{6}) - sin (4 π t + \frac{π}{6})

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

cos (\frac{4}{π} t + \frac{π}{6}), sin (4 π t + \frac{π}{6})

Periodicity of

cos (\frac{4}{π} t + \frac{π}{6}) : \frac{π ^{2}}{2}

Periodicity of

sin (4 π t + \frac{π}{6}) : \frac{1}{2}

Combine periods:

\frac{π ^{2}}{2}, \frac{1}{2}

= π^{2}

What is the periodicity of f(x)=cos(4/pi t+30)-sin(4pit+30) ?
The periodicity of f(x)=cos(4/pi t+30)-sin(4pit+30) is pi^2