Graph each function over a one-period interval.
y = -2 c...

Question

Graph each function over a one-period interval.

y = -2 cos x

Accepted Answer

Graph. The following function considering only one period where our function is Y equals negative six cosine X. We're also given a coordinate plane here to graph our equation on. Now to graph this, we first need the general form of cosine X. This form is given by Y equals a cosine BX. Now we have negative six cosine X which we can use to find our A and RB our A is our amplitude which will be six. Since the negatives in front, this is gonna change how it looks on the graph. Our amplitude itself is just the number six. A period will be two pi divided by B. Now we notice there's no number in front of our X that implies our B as equals to one, meaning our period is just to us. Now, we can find some value supply on our graph by taking XS. Let's say we're starting at X equals zero since we're not shifting to the left or to the right. Now, we notice to find some more points, we can divide our period by four. We will say a period divided by four is two pi divided by four, which gives us pi divided by two. No, we're going to add our pi divided by two to every one of our values. In other words, our first X value X one is pi divided by two plus R zero from before which gives us pi divided by two X two. We will take our previous value pi divided by two and add another pi divided by two to get pie X three will be our previous value. Pi plus pi divided by two to get three pi divided by two. And finally X four will be three pi divided by two plus pi divided by two to get two pi. Now we can find Y values that correspond to our X values make a little table first and we put all of our values. Yeah, we have Y equals negative six. Cosine X you choose zero first, we would get negative six because cosine zero goes to one. If we were to plug in the rest of our values, we would end up getting zero positive 60 and negative six or the rest of our values. Now, we can plot all of these on our graph. We get zero negative six pi divided by 20 56, three pie divided by two zero and two pi negative six. Finally, we connect our points with a smooth curve to get our gra. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each function over a one-period interval.
y = -2 cos x

Key Concepts

Cosine Function

Amplitude

Graphing Transformations

Watch next