srakagoogle.blogg.se - Horizontal shift

As such, the value is equal to 0 if we have the two functions unaltered.

The phase shift (also called the horizontal shift or horizontal translation) describes how far horizontally the graph has been moved from the regular sine or cosine.

and the parts in between are exactly the same (and similarly for the cosine).

For a simple sine or cosine, the period equals 2π since sin(0) = sin(2π) = sin(4π) =.

In other words, the (infinite) graph is just a bunch of period-length copies glued together at the ends.

The period is the length on the horizontal axis, after which the function begins repeating itself.

For a simple sine or cosine, its value is 1 since the centerline is at 0, and the function's values range from -1 to 1.

The amplitude is how far (either way) the values run from the graph's centerline.

Still, it'd be useful to support the visuals with some definitions. To an extent, the picture suggests how they affect the graph. Obviously, those four numbers determine the amplitude, period, phase shift, and vertical shift.

We can write such functions with the formula (sometimes called the phase shift equation or the phase shift formula):įor A, B, C, D arbitrary real numbers, but with A and B non-zero (otherwise, it wouldn't be a trigonometric function). Nevertheless, it's important to remember that many of the notions are more general, especially those of the horizontal translation or the vertical shift.įirst of all, let's look at a picture showing where the amplitude, period, phase shift, and vertical shift appear on the graph (note that the same image appears at the top of Omni's phase shift calculator). As we've mentioned above, we'll be focusing here on trigonometric functions: more specifically on the sine and cosine.