What is the periodicity of f(x)=2cos(5t)-3sin(5t) ?

The periodicity of f(x)=2cos(5t)-3sin(5t) is 2pi

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periodicity of f(x)=2cos(5t)-3sin(5t)

periodicity

f (x) = 2 cos (5 t) - 3 sin (5 t)

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

2 cos (5 t), 3 sin (5 t)

Periodicity of

2 cos (5 t) : \frac{2 π}{5}

Periodicity of

3 sin (5 t) : \frac{2 π}{5}

Combine periods:

\frac{2 π}{5}, \frac{2 π}{5}

= 2 π

What is the periodicity of f(x)=2cos(5t)-3sin(5t) ?
The periodicity of f(x)=2cos(5t)-3sin(5t) is 2pi