How Do You Determine Horizontal Shifts in Sinusoidal Functions?

AI Thread Summary
Determining horizontal shifts in sinusoidal functions involves analyzing the graph's midline and identifying how far it has moved from its standard position. A graph shifted to the right by 15 units indicates that the midline value, which typically occurs at time 0, has been displaced accordingly. Similarly, an 80-unit shift to the right means the midline is now positioned at that new point. Understanding the standard sine function's appearance without shifts is crucial for accurate identification. This method helps clarify how to interpret phase shifts effectively.
DoomBringer2
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1. Hello everyone, I am having some trouble determining precise phase shifting by observing the graphs.

dRt4B.jpg


book says this graph has horizontally shifted to the right by 15 units. How was this determined? I can't figure it out!

second this graph:
hLXCQ.jpg

Says the graph was shifted 80 units to the right but again how is this determined? Please help thnx
 
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Welcome to PF!

Hail DoomBringer2! Welcome to PF! :smile:
DoomBringer2 said:
book says this graph has horizontally shifted to the right by 15 units. How was this determined? I can't figure it out!
…
Says the graph was shifted 80 units to the right but again how is this determined?

Concentrate on the middle of the graph …

at zero phase shift, it should have that middle value at time 0. :wink:
 
Hint: What does the normal sin function look like without any left or right shifts?
 
thanks a lot guys and gals, I am about to submit my work. hopefully I got it right lol
 

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