Question

What is the frequency of `f(t)= sin 12 t - cos 54 t`?

Answer 1

Find the overall period by finding least common multiple of the two periods. The overall frequency is the reciprocal of the overall period.

Explanation:

Let `tau_1 =` the period of the sine function `= (2pi)/12`
Let `tau_2 =` the period of the cosine function `= (2pi)/54`

`tau_("overall") = LCM((2pi)/12, (2pi)/54) = (pi)/3`

`f_("overall") =1/tau_("overall")= 3/pi`