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.

Answer 1

@jim_thompson5910 can you help me on this one too?

Answer 2

what is the period?

what is the phase shift?

Answer 3

If you're not sure, then in general

if y = A*cos(Bx - C) + D

then the period is T = 2pi/B and the phase shift is C/B

Answer 4

@jim_thompson5910 what do you do after figutingout period anf shift??

Answer 5

@wio how do you do this??

Answer 6

what did you get for the period and phase shift?

Answer 7

i got a pi for period

Answer 8

B = 1

T = 2pi/B

T = 2pi/1

T = 2pi

Answer 9

so the period is 2pi

Answer 10

that means that your window must be 2pi units wide to see a full period (from start to end)

Answer 11

ohh yea

Answer 12

now what's your phase shift?

Answer 13

3/1 sp 3??

Answer 14

*so

Answer 15

w = phase shift

w = C/B

w = (pi/3)/1

w = pi/3

Answer 16

this means that the graph of cos(x) has been shifted to the right pi/3 units

Answer 17

ah-ha!!

Answer 18

so you can start at pi/3 and go 2pi units to get to pi/3 + 2pi = pi/3 + 6pi/3 = 7pi/3

Answer 19

making

xmin = pi/3

xmax = 7pi/3

that will give you a window that's wide enough to see exactly one period

Answer 20

ohhhh okay!!! thank you so much!!!

Answer 21

np