Match each function in Column I with the appropriate description in Column II.

I
y = 3 sin(2x - 4)

II
A. amplitude = 2, period = π/2, phase shift = ¾
B. amplitude = 3, period = π, phase shift = 2
C. amplitude = 4, period = 2π/3, phase shift = ⅔
D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

Question

Match each function in Column I with the appropriate description in Column II.

I

y = 3 sin(2x - 4)

II

A. amplitude = 2, period = π/2, phase shift = ¾

B. amplitude = 3, period = π, phase shift = 2

C. amplitude = 4, period = 2π/3, phase shift = ⅔

D. amplitude = 2, period = 2π/3, phase shift = 4⁄3

Accepted Answer

Welcome back. Everyone. In this problem, we want to find the amplitude period and a phase shift of the trigonometric function Y equals eight multiplied by the sine of 11 X minus six. For our answer choices. A says the amplitude is eight, the period is 2/11 of pi and the phase shift is 6/11 units to the right. B says the amplitude is eight, the period is 11 halves of pi and the phase shift is 6/11 units to the right. C says its amplitude is six, its period is 8/11 of pi and the phase shift is eight units to the right. And the D says the amplitude is six, the period is 11 8th of pi and the phase shift is 11 6, 11 6th units to the left. Now, here we're trying to find various parameters from our trigonometric function. OK. So if we're going to figure out what those things are, we need to ask ourselves what we know about the sine function. So what does a sine function usually look like? Well, generally we can recall that every sine function is written in a form Y equals a multiplied by the cosine or sorry. In this case, the sine, right, the sine of BX minus C plus D OK. Where A helps us to find our amplitude because the amplitude of our function is going to be equal to the magnitude of A right B helps us to find our period. Because the period of our function that is the difference between the peaks in our in our function is equal to two pi divided by the magnitude of B for the sine function C tells us the phase shift of our function. In this case, how much it moves to the left to our right, which we can find by dividing C by B and D is our vertical shift. That is how much our graph moves up or down. So if we can write our equation or if we can look at our equation in this form, then we should be able to tell the values of ABC and D and thus figure out our amplitude period and phase shift. So let's compare our graphs. So we know that we're given the function Y equals eight, multiplied by the sine of 11 X minus six. OK. So if we compare both, notice that it's written in the general form and since it's written in the general form, then here we can tell that A, the coefficient of the S term equals it right B which is the coefficient of the X term equals 11 right C which is the term inside our bracket. In this case, it equals six and then there's no constant being added to the S term. So D equals zero. So now that we have the values of ABC and D, then we will be able to go ahead and find the amplitude, the period and the phase shift. Because now this tells us that our amplitude equals the magnitude of eight, which is simply eight. OK, our phase shift, right? Or rather our period rather, our period is going to be equal to two pi divided by B. So that's two pi divided by 11. And because it's positive, well, that doesn't have anything to do with it. Sorry, the period is two pi divided by 11 or 211, soft pi. And then finally our fields shift, our phase shift is going to be equal to C divided by B which is six, divided by 11. And because it's positive, that means our graph is going to move 6/11 units to the right. So for our graph, our amplitude is it, our period is 2/11 of pi and it's going to move six to the 11th, 6/11 units to the right. If we look back on our answer choices, that would have been answer choice. A thanks a lot for watching everyone. I hope this video helps.

Verified Solution

Key Concepts

Amplitude

Period

Phase Shift