period of function ; cos cube 3x+ tan 4x

Question

period of function.

Answer 1

The function is .

If is function and  , then is said to be periodic function.

Here P is the period of the function.

is a composite of cubic function and cosine function.

Horizontal stretch of     is 3.

The relation between stretch and the period P of cosine function is , B is stretch.

So, the period of is .

The stretch of is 4.

The relation between stretch and the period P of tangent function is , B is stretch.

So, the period of is .

The LCM of gives the period of .

LCM of is .

So, the period of is .

The graph of one period of the function is

Comments

The LCM of is

(2pi)/3=120

(pi)/4=45

LCM of 120, 45 is 360 i.e 2pi

Therefore, The LCM of is .