Trig Project - When math is not math.

[MacLaddy]

Homework Statement

Math is not math when it asks me to describe relationships between functions. I hate wordplay.

Please see the attached PDF. On this page it says "What relationship between the cosine and secant do the graph and these values suggest?"

Homework Equations

Well, the paper speaks of using MAPLE, but the teacher instructed us just to use our calculators. So that throws some things off.

The Attempt at a Solution

I'm not sure what it's asking here. Do you think they are just speaking of the fact that they are reciprocals of each other, or perhaps that the secant approaches infinity as the cosine approaches zero?

Any help would be appreciated. Following this question is the same thing for the sin/csc, and the tan/cot. I consider myself a methodical person in trying to figure things out and making sure things turn out well, but questions like this always throw me off.

 

[jhae2.718]

I'm not sure what it's asking here. Do you think they are just speaking of the fact that they are reciprocals of each other, or perhaps that the secant approaches infinity as the cosine approaches zero?

I'd say most likely the relationship wanted is $$\sec(\theta)=\frac{1}{\cos(\theta)}$$, as you said.

 

[MacLaddy]

I'd say most likely the relationship wanted is $$\sec(\theta)=\frac{1}{\cos(\theta)}$$, as you said.

Thank you for your quick reply.

It seems to simple for me. I guess perhaps I tend to make things more complicated then they are.

 

[jhae2.718]

Thank you for your quick reply.

It seems to simple for me. I guess perhaps I tend to make things more complicated then they are.

You're not the only one with that problem.

What is the course?

Here's a plot I made in MATLAB, just for reference.

 

[MacLaddy]

You're not the only one with that problem.

What is the course?

Just standard Trigonometry. I never took it in high school so I do not know if there are different levels, but this is all that's needed for my EE requirements.

I am going to ask one more question in this same project, if you don't mind. Are you familiar with MAPLE? I ask because I think it may have something to do with this.

The very last question tells me to plot the following functions,

$$0.6\sin(1.5x)+\cos(1.5x-\frac{\pi}{3})$$
$$1.2\sin(2x)+\cos(x+\frac{\pi}{3})$$
$$0.6\sin(1.5x)+\cos(2x-\frac{\pi}{3})$$
$$0.6\sin(2x)+\cos(x-\frac{\pi}{3})$$

It says to Plot each of these in MAPLE, and to see how they affect the graph. After I graph at least twenty variations of the problem I need to write one or two paragraphs explaining how I observed the graphs change with the changes in the constants of the functions.

Stuff like this really drives me nuts. Not sure how other people feel about these "objective observations" in math.

 

[MacLaddy]

Here's a plot I made in MATLAB, just for reference.
View attachment 33365

I'm not familiar with MATLAB. That's a nice graph, I'll have to look into that program.

 

[jhae2.718]

I'm afraid I'm not a MAPLE user. At my university, engineering students use MATLAB for mathematics courses. The MAPLE http://www.maplesoft.com/support/help/Maple/view.aspx?path=plot" might be helpful, though.

I'm assuming you have to plot twenty permutations of some function $$f(x)=a\sin(bx)+\cos(cx+d)$$?

 

[MacLaddy]

I'm afraid I'm not a MAPLE user. At my university, engineering students use MATLAB for mathematics courses. The MAPLE http://www.maplesoft.com/support/help/Maple/view.aspx?path=plot" might be helpful, though.

I'm assuming you have to plot twenty permutations of some function $$f(x)=a\sin(bx)+\cos(cx+d)$$?

I believe it is looking more for a description on how I have "observed the graphs change with the changes in the constant of the function." It's just asking me to explain what I am observing on how the graph changes.

Not sure. It's moving, stretching, compressing, shifting. I don't know how I can get two paragraphs out of it.

 

[MacLaddy]

This knocked a bit out of the scan, but I think you will understand my meaning better from the attached PDF.

 

[jhae2.718]

Well, you can talk about the change in amplitude given by the constants in front of the trigonometric functions, the translations resulting from constants added to the functions and to the arguments (e.g. y = sin(x+a)+b, describe how a and b affect y), how the constants multiplied with x affect the period...

 

[MacLaddy]

Well, you can talk about the change in amplitude given by the constants in front of the trigonometric functions, the translations resulting from constants added to the functions and to the arguments (e.g. y = sin(x+a)+b, describe how a and b affect y), how the constants multiplied with x affect the period...

Ah, yes. Once again I am over-complicating things. I was thinking more in terms of one function changing and "pulling/pushing" the other function with it.

Thank you, jhae2.718. I truly appreciate your help. I accomplished all 10 pages of the project in one afternoon, and have been stuck on the four word problems for three days. I don't think I'm wired correctly for questions like that.

 

[jhae2.718]

Ah, yes. Once again I am over-complicating things. I was thinking more in terms of one function changing and "pulling/pushing" the other function with it.

That is another thing you can write about; the sine and cosine terms will affect each other. (Sine terms will have the most effect near points where the argument for sin is close to +/- pi/2, and cosine where the argument for cos is close to zero, or n*pi.)

 

[MacLaddy]

That is another thing you can write about; the sine and cosine terms will affect each other. (Sine terms will have the most effect near points where the argument for cos is close to +/- pi/2, and cosine where the argument for cos is close to zero, or n*pi.)

Definitely thank you for that. I knew that they had an effect on each other, but I couldn't puzzle out why by looking at the graph. Makes perfect sense now that you've said it. I imagine they will cover that later in the class, but considering I have barely over a month left, they may not.

 

[jhae2.718]

I typo'd, by the way. That should have read "Sine terms will have the most effect near points where the argument for sin is close to +/- pi/2 ..."

Hope that helps.

 

[MacLaddy]

It helps greatly. Thank you again.