Determine the number of cycles the function has on the interval from 0 to 2 pi. Also state its amplitude and period

Question



Answer 1

lets imagine the function of interest is in form of

Y= A sin( B( X-C))+ D Or Y= A cos( B( X-C))+ D

A is the value of the amplitude

( 2 pi) ÷ B is the period of the graph so B is the number of cycles between 0-2 pi

C is the horizontal movement of the graph

D is the vertical movement of the graph

Example:

Y= 2 sin 3X

it has an amplitude of 2 and a period of 2pi/3

it has 3 cycles of sin in between 0 and 2pi