In Exercises 61–66, use the method of adding y-coordinates to gra...

Question

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π.y = cos x + sin 2x

Accepted Answer

Graph, the function for zero less than equals to X less and equals to two pi by performing the addition of Y coordinates where Y equals three cosine X plus sign of two X. They were also given a coordinate plane to graph up. Now it says by performing the addition of Y coordinates. So we can split up our Y equals, we'll split it up into Y one plus Y two where Y one is three cosine xy two is sine two, X. Let's make a table of values. Now we will create an X column A Y one, A Y two and A Y one plus Y two where our points will be XY one plus Y two. And we'll just use the X values on our graph zero. I divided by four, I divided by two, three pi divided by four pi five pi divided by four, three pi divided by 27 pi divided by four. And finally, the bottom two pi now we can plug in these values. Our first one is three cosine X plug in our values. So you plugged in zero, first with first three. So you'd have Y one equals three cosine of zero. We cannot repeat the process for every one of our X values 2.1 zero, negative 2.1 negative three, negative 2.10 2.1 positive three. Was it the same for Y two or sine to X? You get zero 10, negative 1010, negative one and zero. Finally, we can add all of these together for Y one plus Y two. The first one, you will get three plus zero, which is just three, 2.1 plus one gives us 3.1 zero plus 00. Then we get negative 3.1 negative three, neither 1.1 01.1 and three. Now we have our X column and our Y one plus Y two column. We can plot each of these as points. For example, our first point would be 03. Our second would be pi divided by 43.1. We will plot all of these onto the graph. So we have a point 03 pi divided by 43.1 pi divided by two and zero 35 divided by four, negative 3.1 pi negative three by pi divided by four negative 1.1 three pi divided by two and zero 75 divided by four positive 1.1. And finally two pi three, we can then make a smooth curve between all of our points. The other graph that looks something like this. Ok. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 61–66, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π.y = cos x + sin 2x

Key Concepts

Trigonometric Functions

Graphing Techniques

Periodicity and Amplitude

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