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

1 Answer
Jun 30, 2016

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.#