In Exercises 14–15, use the method of adding y-coordinates to gra...

Question

In Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π.

y = sin x + cos 1/2 x

Accepted Answer

Graph, the function on the interval 0 to 2 pi for X by adding the Y coordinates, our equation is Y equals sine two X plus cosine 1/ X. Now the graph this, let's first split up our equation Y into Y one and Y two or Y one is signed two XY two is cosine 1/4 X. So to graph this, we will add these equations together. Let's make a table of potential values. XY one NY two X, let's say we use zero pi divided by four pi divided by 23 pi divided by four hi five pi divided by 43 pi divided by two, seven pi divided by four. And finally two pi. Now we will plug each of these X values into our equation. For example, the first one would be zero. That would be sine of two multiplied by zero, giving us sign zero, which we know sign of zero is going to be zero will do the same thing for every one of these values to fill out the rest of them. It's 10, negative 101 zero and you live 10. Now we can do the same for Y two cosine 1/4 X. If we were to plug it in, we get one 0. 0.90 0. 0.70 0.60 0. 0.2 and zero. Finally, we can add these together, Y one plus Y two, 11.980 0. negative 0.20 0.71 0. 0.4 0.8. And finally zero. Now you can create a point out of xy one plus Y two. Our first plan would occur at zero and one. So you put the point and X equals zero, Y equals one. We will do the same for every point after we have 11.98 or rather pi over four, we should say not one but pi divided by 41. pi divided by 20.9 three pi divided by four, negative 0.2 pi 0. five pi divided by 41. three pi divided by 20. seven pi divided by 40.8. And finally two pi zero, we can now connect all of these points with a smooth curve and we have our graph of the function. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 14–15, use the method of adding y-coordinates to graph each function for 0 ≤ x ≤ 2π. y = sin x + cos 1/2 x

Key Concepts

Trigonometric Functions

Graphing Techniques

Periodicity

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