Question

What is the period of the graph of the equation y= 3 cos 4x?

Answer 1

the period of the given fun. is `pi/2.`

Explanation:

We know that the Principal Period of cosine fun. is `2pi.` This means that, `AA theta in RR, cos(theta+2pi)=costheta.......(1)`

Let `y=f(x)=3cos4x`

But, by `(1), cos4x=cos(4x+2pi)`

`:. f(x)=3cos4x=3cos(4x+2pi)=3cos{4(x+pi/2)}=f(x+pi/2),` i.e., `f(x)=f(x+pi/2)`.

This shows that the period of the given fun.`f` is `pi/2.`