If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x pi/3), what should be used f
Mathematics
bosslegend
Question
If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x pi/3), what should be used for Xmin and Xmax? Explain your answer.
2 Answer

1. User Answers LammettHash
The period of a sinusoid [tex]\cos 2(xc)[/tex] is [tex]\dfrac{2\pi}2=\pi[/tex], so any range such that [tex]\mathrm{Xmax}\mathrm{Xmin}=2\pi[/tex] will give two complete periods. 
2. User Answers erinna
Answer:
The smallest possible domain to completely graph two periods is either [0, 2π] or [π, π].
Stepbystep explanation:
The period of cosine function [0, 2π].
The given function is
[tex]y=5+3\cos 2(x\frac{\pi}{3})[/tex]
This function can be written as
[tex]y=5+3\cos (2x\frac{2\pi}{3})[/tex] .... (1)
The general form of cosine function is
[tex]y=A\cos (Bx+C)+D[/tex] .... (2)
where, A is amplitude, [tex]\frac{2\pi}{B}[/tex], C is phase and D is midline.
From (1) and (2), we get
[tex]A=3,B=2C=\frac{2\pi}{3},D=5[/tex]
[tex]Period=\frac{2\pi}{2}=\pi[/tex]
The period of given function is [0,π]. So, the smallest possible domain to completely graph two periods is either [0, 2π] or [π, π].