# What is the period of #f(t)=sin( t / 36 )+ cos( (t)/ 42) #?

##### 2 Answers

#### Explanation:

First of all we, know that

From this, we can deduct that

In your case,

Your global function is the sum of two periodic functions. By definition,

and in your case, this translates into

From here, you can see that the period of **both** terms to do a whole turn, we need to take the least common multiple between the two periods:

#### Explanation:

The least positive P (if any ) such that f( t + P ) = f( t ) is befittingly

called the period of f(t). For this P, f(t+nP)=f(t), n =+-1,, +-2, +-3, ...#.

For

For

Here,

the period for

for

For the given compounded oscillation f(t), the period P should be

such that it is also the period for the separate terms.

This P is given by #P=M(pi/18)=N(pi/21). For M= 42 and N= 36,

Now, see how it works.

#=f(t).

If halve P to 761 and this is odd. So, P = 1512 is the least possible

even multiple of