Graph each function over a two-period interval. Give the perio...

Question

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.

y = 2 sin ¼ x

Accepted Answer

Draw the graph of the function given below consider only two periods and also determine the period and amplitude where our function is Y equals four sine one half X. And we're given a coordinate plane to graph our function on now to graph this, we need the general form of a sine equation. That general form is given by why equals a sin BX where A is our amplitude and B will be the value we used to fund our period period is given by the equation two pi divided by B we see in our function A as equals to four B as equals to one half. This makes our period equals to two pi divided by one half which gives us four pie. Now we can find some X values to plot on our graph. Let's say we take X one as equals to zero. Since we're not shifting to the left or to the right. To find our next points, we can divide the period by four to get four equal parts. So X two would be our previous value X one plus our period divided by four period divided by four in our case or pi divided by four, which is just pi, meaning our X two will be zero plus pi which is just pi X three will take our previous answer pi and add another pi which gives us TP we will do the same for our next values. X four will be two pi plus pi which gives us repay. And finally, our last point we want five will be three pi plus pi which is four P. Now we have all of our X values. We can now find output Y values. Still plot on our graphs. We will make a table. We put all of our values here and we will find are wise by plugging in the X values. We have four. So one have X which you can plug in our first X value being X equals zero. This gives us or sign of zero which is zero, meaning our first one, this is why equals zero, we can do the same for all of our values. We plugged in pi next we would get fours pi divided by two which just gives us four. If we were to fill out the rest of the values, we get zero negative four and zero. Now we can plot our points on the graph. We have our 1st 0.00 a second point P four, our next 0.2 pi zero three pi negative four and finally 40. Now because this is a sign graph, it's going to loop once it's finished with its full period. Meaning if we were to continue, we'll go to our next value. Five pi, that value will be four, 65 will be zero seven pi will be negative four and eight pi will be zero. We can now draw a smooth curve between all of our points starting from 00. We go up, back down, back up, back down again and finally back up. That is the graph of Y equals four sine one half X. OK. Hope to help you solve the problem. Thank you for watching. Good bye.

Graph each function over a two-period interval. Give the period and amplitude. See Examples 2–5.
y = 2 sin ¼ x

Key Concepts

Period of a Trigonometric Function

Amplitude of a Trigonometric Function

Graphing Trigonometric Functions

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