# What is the period of f(theta)= sin 3 t - cos 5 t ?

period $= 2 \pi$

#### Explanation:

$f \left(t\right) = \sin 3 t - \cos 5 t$

for $\sin 3 t$ the period ${p}_{1}$

${p}_{1} = \frac{2 \pi}{3} = \frac{10 \pi}{15}$

for $\cos 5 t$ the period ${p}_{2}$

${p}_{2} = \frac{2 \pi}{5} = \frac{6 \pi}{15}$

Another number which can be divided by both ${p}_{1}$ or ${p}_{2}$ is $\frac{30 \pi}{15}$

Also $\frac{30 \pi}{15} = 2 \pi$

therefore the period is $2 \pi$