determining phase shift of a periodic function from diagram

[fred2028]

Given a diagram of a sinusoidal curve, how can one determine the phase shift in the following equation:

f(x) = a sin[p(x - h)] + k

...where p is the phase shift?

Currently I can only do it by looking at the graph and counting the squares, but if there is a way to do it algebraically then please teach me

 

[skeeter]

f(x) = a sin[p(x - h)] + k

"p" does not give the phase shift ... for sine and cosine, (2pi)/|p| = the period.

"h" gives the phase shift ... for h > 0, (x + h) is a phase shift to the left "h" units.
(x - h) is a phase shift to the right "h" units.

|a| is the amplitude

"k" is the vertical shift

 

[fred2028]

f(x) = a sin[p(x - h)] + k

"p" does not give the phase shift ... for sine and cosine, (2pi)/|p| = the period.

"h" gives the phase shift ... for h > 0, (x + h) is a phase shift to the left "h" units.
(x - h) is a phase shift to the right "h" units.

|a| is the amplitude

"k" is the vertical shift

Oh damn, sorry, I meant variable h ...