In Exercises 67–68, use the method of adding y-coordinates to gra...

Question

In Exercises 67–68, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 4.

y = cos πx + sin π/2 x

Accepted Answer

Draft the function on the interval 0 to 2 pi or X by performing the addition of Y coordinates, Y equals cosine two by X plus two sine by X divided by three. And we have a coordinate plane to graph our function on. Now what we can do first as we can determine our equations as Y equals Y one plus Y two where Y one will be cosigned to pi X. Why two will be two sin by X divided by three? No, we can plug in some values for our equation. Let's make a table we have X Y one, Y two and Y one plus Y two. Now let's find some values to plug in I. So I use X is zero 0.5. What? 1.5 two, 2. 33. and four. And finally, at the end, I will put a two pie. Just demonstrate how we can do this. Now, we will first fill out the Y one column which uses cosine two pi X. Other words, we would have cosine two pi of our first X which would be zero. If we simplify that we would get one. Now we can plug these values in and fill out the rest of the table. It probably fill off the table with the calculator. But for now, we will just do these values for every 0.5. On this equation, we alternate between one and negative one. Finally, for two pi at the very end that gives us negative 0. we'll do the same for Y two. We plug in our value into Y two. Our first one would give us zero. Our next one will give us one. Then we have 1. and two one. Then we have zero negative one, negative 1.73. And finally, for two, we get 0.6. It looks like I skipped 2.5 or two, actually skipped two. Here two would be 1.73 and 2. would be one. Now, Y one plus Y two will add these equations together. So we'll add our Ys together. We get one 02173, 12.73 01, negative two, 0.73 negative and 0.4. Now, we have a table of values, we can plot this onto our graph. Now, I actually found some more values just to see what the graph looks like. But we start at 01, X is zero, ry, one plus Y two is one and this graph looks a little bit weird. Pull the door down. Go up, wave a little bit at the top, touch the axis again. So up, time down what? Down, back up again. I love it down again and back up to pi how we can find this graph by just finding more values of X and plugging them in. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 67–68, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 4. y = cos πx + sin π/2 x

Key Concepts

Trigonometric Functions

Graphing Techniques

Periodicity

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