For each function, give the amplitude, period, vertical transl...

Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = -sin (x - 3π/4)

Accepted Answer

Welcome back everyone. In this problem, we want to determine the amplitude period phase shift and vertical translation of the trigonometric function Y equals negative sine of X minus 7/12 of pi. For our answer choices, A says the amplitude is one, the period is two pi the phase shift is 7/12 of pi units to the right. And there is no vertical translation. B says the amplitude is one, the period is two pi the phase shift is 7/12 of pi units to the left and the vertical translation is 7/12 units up. C says the amplitude is one, the period is 14 pi the phase shift is 7/12 of pi units to the right and the vertical translation is none. And the D says the amplitude is 12 7th. The period is 14 pi the phase shift is 7/12 of pi units to the left and the vertical translation is none. Now, if we want to figure out these parameters, we need to think about how they relate to the sine function. So what we need to ask ourselves is what do we know about the sine function that can help us to find amplitude period phase shift. And vertical translation will recall that every sine function is basically written in the general form a multiplied by the S of BX minus C OK plus D, right? Where A helps us to find our amplitude because our amplitude equals the magnitude of A, right B helps us to find our period. Let's bring that note a bit, helps us to find our period because our period equals two pi divided by the magnitude of B C helps us to find our fear shift because our fear shift equals C divided by B and D helps us to find our vertical translation. Because D, well, B is a vertical shifter or vertical translation. OK. So what does this tell us? Well, if we can figure out the values of ABC and D from our equation, then we should be able to find our amplitude period phase shift and vertical shift. So let's do that. So let's write down our trigonometric equation here which we know was Y equals negative sine multiplied by X minus 7/12 7 12th of pi. I'm going to write it that way, 7/12 of pi. Now when we look at our general form and our equation notice that basically both of them are in the same form here. I could probably add that for a negative sign, I could probably put a one there to show that it would have been the coefficient is negative one. But essentially they are in the same form. So from it, we can tell our values of ABC and D because now this tells us that A equals negative one. OK. B the coefficient of X equals one C equals 7/12 or 7/12 of pi rather. And D, well, we don't have any constant here, so D equals zero. So now let's use these things to help us find our, our, our parameters because no, this means that our amplitude equals the magnitude of negative one, the magnitude of A which is one. OK. Our period equals two pi divided by B. So that's two pi divided by one which is two pi OK. And our phase shift, our phase shift equals C divided by B. So that is 7/12 of pi divided by one, which would just be 7/12 of pi and our vertical shift D equals zero. So from our equation, we can tell that its amplitude is one, its period is two pi and its phase shift is 7/12 of pi. So that because it's positive, it would be 7/12 of pi to the right. So when we look back on our answer choices, the correct choice would be answer choice. A thanks a lot for watching everyone. I hope this video helped.

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = -sin (x - 3π/4)

Key Concepts

Amplitude of a Sine Function

Period of a Sine Function

Phase Shift and Vertical Translation

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