Feb 17, 2019 · $\begingroup$ One can assign many phase shifts to the same function, each of which will produce the same graph. Take any phase shift and add or subtract any multiple of the period and that will produce another valid phase shift. But ideally the best value to use for the phase shift is the one with smallest absolute value.

To figure out the vertical shift, what would you do to a function centered on the x axis to achieve the given graph. In this case you are adding 1. (going from a function with a range of $[-2,2]$ to $[-1,3]$) Then a simple way to find a phase shift is to look at the part of the graph that would normally correspond to $\cos(0)$.

Dec 2, 2014 · I am now trying to find the phase shift. I moved the 'working x-axis' 2 units down, in accordance with the vertical displacement of -2. Since the cosine function starts at 1 on the y-axis, how do I find the phase shift. If the x-axis is at -2, then the point where y=1 is a tiny fraction of a unit away from the y-axis. So how do I find the phase ...

Sep 25, 2024 · What is a phase shift in trigonometry, and how can I determine them given a graph? 0 Sine regression phase shift with known amplitude and period from data points

Dec 7, 2018 · Why does the horizontal phase shift of: $ 2\sin(-3x-\frac\pi2) $ shift to the right instead of to the left ...

In a function like $\\sin(2x + 3)$ why is the phase shift $\\frac{3}{2}$ units to the left instead of 3 units to the left

I understand phase shift as the shift from $ sin(2x) $, and in a graph it is plain that the actual phase shift $ \frac{\pi}{3} $! $\endgroup$ – lericson Commented Oct 4, 2013 at 16:38

Aug 31, 2023 · Check this resource for some nice pictures and term descriptions, but using the curves you have $$ y_1 = 2\sin\left(\frac{x}{2}+\frac{\pi}{2}\right) = 2\sin\left(\frac{1}{2}\left(x+\pi\right)\right) $$ so the phase shift here is $\pi$, not $\frac{\pi}{2}$ as we need to remove the stretch term first before we can see the shift.

Feb 3, 2022 · For the left-moving wave, +, $\phi_+$ is the amount you need to shift the true origin of the cycle, x=2, to the left, to position it at the crossing of the axes, in your left graph. For the right-moving wave, $-$ , you need to do the same to x =5, by $-\phi_-$ to get minus the standard cycle, as dictated by the above sine function.

Aug 24, 2015 · Fourier transform of a sum of phase-varying Gabor wavelets 0 What is the Fourier cosine transform in complex notation and what is the conjugate of the Fourier cosine transform?