Graphing x(t): Simple Stretch & Translation

[Karma]

For the Graph...

x(t)=1+2cos(pi/3(t+1))

First i just draw a graph of cos and than... It is just a simple stretch of 1 in the y-direction and a translation of 1 to the left ... correct?

 

[Dick]

No. Why don't you just start plugging some values of t in and draw the graph? How it's related to cos should then start to become clearer.

 

[Karma]

What does the 1 in the beginning of the equation represent dick?

 

[Dick]

The 1 is a translation up one unit in x (which you could consider the 'y' direction - depending on how you draw your graph). It's not a 'stretch' and it's not to the left.

 

[Karma]

And the Period has the equation 2pi/B...what would the "B" represent in my equation dick? would it be pi/3? ... and how would i calculate what the new zeroes of the graph would be?

 

[Dick]

If you would actually start plotting the graph instead of thinking about doing it this would become apparent. The period would be the increment in t that you need to make pi/3*(t+1) change by 2pi. What might that be? To get the new zeros of your graph solve for x(t)=0.

 

[Karma]

thanks a lot dick..it also states find all values of t with 0<t<20 such taht x(t)=x(0)...so basically all the values of t in this situtation ...are those values that hit 0 on the x-axis ...correct?

 

[Dick]

Absolutely.