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 = 2 sin (x + π)

Accepted Answer

Welcome back, everyone. In this problem, we want to determine the amplitude period phase shift and vertical translation of the given trigonometric function Y equals 18 multiplied by the sine of X plus 1/7 of pi. For our answer choices. A says the amplitude is nine, the period is two pi the phase shift is 1/7 of pi units to the right. And the vertical translation is one unit up. B says the amplitude is nine. The period is half of pi the phase shift is 1/7 of pi units to the right. And the vertical translation is one unit up. C says the amplitude is 18. The period is two pi the phase shift is 1/7 of pi units to the left and no vertical translation. And D says the amplitude is 18. The period is a half of pi the phase shift is 1/7 of pi units to the left and no vertical translation. Now let's ask ourselves what we're really trying to figure out here. We're trying to determine each of these parameters from our trigonometric function for science. So to help us understand the parameters, we have to ask ourselves what do we know about the sine function? Well, recall that the general form of a sine function. In other words, every sine function says that Y equals a multiplied by the S of BX minus C plus D. This is what every sine function looks like where A helps us to figure out the amplitude of our function because the amplitude is the absolute value of A. Right B helps us to figure out the period of the function because the period equals two pi divided by the magnitude of B for the sine function C helps us to figure out our phase shift because our phase shift is equal to C divided by B OK. And D helps us to figure out our vertical shift because well, D is the vertical shift. So if we can compare our equation that we have to the general form, we should be able to find the values of ABC and D and thus figure out all of these parameters. So what do we know? Well, our function is Y equals 18 multiplied by the sine of X plus 1/7 of pi. No, we can't compare it to the general form just yet because notice that it doesn't exactly look like the general form completely in the general form. We're subtracting C from the X term, but in this case, we're adding our, our term to X. So we'll need to rewrite it where we'll be subtracting from X. How can we do that well, to add 1/7 of pi is the same thing as subtracting its negative value. So we can rewrite our function then as Y equals 18 multiplied by the sine of X minus a negative seventh of pi. Because when we subtract the negative seventh of pi is the same thing as adding 1/7 of pi. No, we notice that the general form looks like our equation. OK? And know that it looks like our equation. By comparison, we can tell that A equals 18. OK. B the coefficient of X equals one and C or term C as being subjected is negative 1/7 of pi. So now that we have those in that information, we will be able to find the amplitude period and a phase shift notice as well. There is no constant being added to our sine function. So that tells us that there is no vertical translation. So let's use what we know from what we know. OK. This tells us that our amplitude which equals the magnitude of A will be the magnitude of 18 which is 18. Next, we know that our parents is going to be two pi divided by B. So that's two pi divided by one. Let's write the pi properly here, two pi divided by one which is two pi and our fears shift. OK. Our fears shift is going to be equal to C divided by B. So that's a negative seventh of pi divided by one, which would just be a negative seventh of pi. And because it's negative, that tells us that we're going to be moving 1/7 of pi units to the left. So our equation tells us that our amplitude is 18, our period is two pi and we're going to move our graph 1/7 of pi units to the left. When we look back on our answer choices that would have been answer choice. C 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 = 2 sin (x + π)

Key Concepts

Amplitude of a Sine Function

Period of a Sine Function

Phase Shift and Vertical Translation

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