What is the period of $f (t) = sin (\frac{t}{30}) + cos (\frac{t}{6})$ $f(t)=sin( t / 30 )+ cos( (t)/ 6 )$ ?

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Answer 1 · 2016-04-02T14:11:37

#60pi.

The period of sin kt is $2 \frac{π}{k}$ $2pi/k$ and so is the period of cos kt..

Here, the period of $sin (\frac{t}{30}) = 60 π$ $sin (t/30) = 60pi$ and the period of $cos (\frac{t}{6}) = 12 π$ $cos (t/6)=12pi$ .

So,. the period of the sum is the least common multiple of the separate periods = $60 π$ $60pi$ .

What is the period of f(t)=sin( t / 30 )+ cos( (t)/ 6 ) f(t)=sin(t30)+cos(t6)f(t)=sin( t / 30 )+ cos( (t)/ 6 ) ?