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

Question

1648 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-10T20:02:02

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

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

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

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

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