Chapter 8.8, Problem 24P

Table entries L28 and L29 are known as translation or shifting theorems. Do Problems 19 to 27 about them.

Sketch on the same axes graphs of $\sin t,\sin (t-\pi /2),$ and $\sin (t+\pi /2),$ and observe which way the graph shifts. Hint: You can, of course, have your calculator or computer plot these for you, but it’s simpler and much more useful to do it in your head. Hint: What values of $t$ make the sines equal to zero? For an even simpler example, sketch on the same axes $y=t,y=t-\pi /2,y=t+\pi /2$.