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Shared with meShow My Work (Optionan @DETAILSMCKTRIG8 4.T.008_For the equation below first identify the amplitude and perioc3 cos XamplitudeperiodUse this informat...

Question

Shared with meShow My Work (Optionan @DETAILSMCKTRIG8 4.T.008_For the equation below first identify the amplitude and perioc3 cos XamplitudeperiodUse this information sketch one complete cycle of the gra

shared with me Show My Work (Optionan @ DETAILS MCKTRIG8 4.T.008_ For the equation below first identify the amplitude and perioc 3 cos X amplitude period Use this information sketch one complete cycle of the gra



Answers

Determine the amplitude, period, and displacement for each ficnction. Then sketch the graphs of the functions. Check each using a calculator: $$y=30 \cos \left(\frac{1}{3} x+\frac{\pi}{3}\right)$$

So we're going to start with to function. Why is equal to negative sign three X a minus pirate. You. Okay. And that gives us a magnitude or an amplitude Equal to the absolute value of a. Which in this case is just gonna be one period of two pi over B. Which in this case is going to be to pi over three and then a displacement of negative C over B. That's just going to be positive pi over 2/3 which is positive pi over six. So we could look at our graph, we see the amplitude of one, we see that it was shifted right here, shifted five or six units to the right. And then we see that based on this hour period is going to be exactly um two pi over three. So that's our final answer.

So for this problem we're starting off with the equation Y equals hi co sign. Mhm. One over pie at plus one third. So with these values in mind we first want to find the amplitude which is the active value of eggs. So this is just gonna be pi and we want to find a period which is two pi over be So it's going to be two pi divided by one over pipe. So it's going to be two pi squared as our period and then our displacement is going to be um negative C over B. So that is a one third or negative one third in this case negative one third divided by one over pie. So it's going to be a negative high thirds. Then confirming this. I will make graphic, we see we're going to get a amplitude of pie. We were displaced by a negative pi over three. Which we also see as the case right here. And then we want to find the period. So we go from negative pi over three To 18.692, which suggests that our period is two pi squared, so this is our final answer.

For this function. The employees to is the number in front of the sign function. The positive value, said the amputees wanted now for period is two pi over and periods the length off one cycle. So for sign graph is two pi over anywhere n Easter number of cycles. So in this case, the number of cycles here is three. So we have two times over tree as the period.

So for this problem we're going to have, why is equal to 1.8 sign of kayaks plus 1/3. Yeah, so that means that the amplitude which is equal to the absolute value of a, it's going to be 1.8 A period which is equal to two pi over B is going to equal just to and the displacement which is equal to um negative C over B is going to give us a negative one third divided by pi. So that's going to be a negative 1, 1/3 pi. Then zooming out to look at our graph. We see that we do have the amplitude of 1.8. The displacement was a negative 1/3 pi and the period itself is going to be um two as we see her, this is a period of two. So we've done everything correctly.


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