Question

1. Define phase shift. Could every sine function be expressed as a phase shifted cosine function? Explain.

Answer 1

yes every sine function can be expressed as a cosine function and vice versa. Phase shift is like a starting point

Answer 2

Phase shift is where the function has an angle offset, i.e.\[\sin{(\theta\pm\phi)}\\\cos{(\theta\pm\phi)}\]As you know, there exists an identity:\[\sin\theta=\cos(\theta\pm\frac\pi2)\]

Answer 3

\[\sin\theta=\cos(\theta-\frac\pi2)\ \text{rather}\]

Answer 4

and all this time, I have been doing it the long hard way.
I always look at the graphs and wrote everything down
wished I had known there was a more efficient way of doing this......
Thanks, next time I do these types of problems, I am going to look up the identity

Answer 5

Phase shift is the horizontal shift for a periodic function.

Answer 6

For example, the function f(x) = 3sin (x – π) has a phase shift of π. That is, the graph of f(x) = 3sin x is shifted π units to the right.