How Do You Determine Horizontal Shifts in Sinusoidal Functions?

[DoomBringer2]

1. Hello everyone, I am having some trouble determining precise phase shifting by observing the graphs.

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:

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

 

[tiny-tim]

Welcome to PF!

Hail DoomBringer2! Welcome to PF!

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.

 

[tal444]

Hint: What does the normal sin function look like without any left or right shifts?

 

[DoomBringer2]

thanks a lot guys and gals, I am about to submit my work. hopefully I got it right lol