Graphing a variation of y=sin-x

[JR Sauerland]

Just have a quick question about this problem in the photo... I'm not sure how they got the values 0, 1, 0, -1, 0 that they are multiplying by y=sin-x in the chart:

For example. Look at the second row, pi/2. They apparently multiply 1/2 by 1 to get 1/2, but they never indicate where/how they are getting the values to multiply by the amplitude of 1/2. I'm guessing, but I don't want to guess, that it is due to the fact that the sin goes up from 0 to 1, down to 0 again, and then all the way down to -1. It seems like they are basing it off of the y-values from this previous page in the text:

Again, not really sure about this. Am I supposed to base it off of the standard values for y=sin-x?

 

[Dr. Courtney]

Do you mean sin(-x)?

Have you tried graphing it?

 

[pbuk]

I'm not sure how they got the values 0, 1, 0, -1, 0 ...

You need to spend more time looking at what is in front of you and less time posting here.

What are the "five key points", i.e. values of $x$, they are referring to? What are the values of $\sin x$ at each of these points?

 

[JR Sauerland]

Do you mean sin(-x)?

Have you tried graphing it?

I put the - as a spacer so to speak rather than leaving it as sinx or sin x

 

[JR Sauerland]

You need to spend more time looking at what is in front of you and less time posting here.

What are the "five key points", i.e. values of $x$, they are referring to? What are the values of $\sin x$ at each of these points?

You are extremely rude and disrespectful, not only to me, but to everyone else you reply to. I have actually spent the last week and a half reading my trigonometry book from cover to cover, 9 hours a day, and I'm on chapter 4. So you telling me to 'spend more time looking at what is in front of me' is a snarky, moot comment.

 

[pbuk]

I am sorry if you find what I say rude and disrespectful, but it is my honest and frank opinion that you need to develop your skills in digesting and drawing inferences from what you are reading rather than asking other people to answer questions for you.

 

[JR Sauerland]

I am sorry if you find what I say rude and disrespectful, but it is my honest and frank opinion that you need to develop your skills in digesting and drawing inferences from what you are reading rather than asking other people to answer questions for you.

I'm not asking anyone to answer a question for me. That's like making a list of my homework problems and posting them with no attempt to solve them. I made a fair inference on how they were getting the information, and asked for confirmation or clarification. You're clearly trying to portray me in a negative light, for whatever reason.

 

[SteamKing]

I put the - as a spacer so to speak rather than leaving it as sinx or sin x

Using the "-" as a spacer is confusing, especially since "-" can indicate negation of a quantity or subtraction of two quantities.

If you want to clarify your math expressions, use parentheses " ( ) " or brackets " [ ] ". e.g. y = sin (x), rather than y = sin -x .

Now, as to your original question, for y = sin (x), y can have values between -1 and 1. Thus, the amplitude of the sine function is 1, as can be seen below:

​

If you multiply the sine function by a constant A, then all the values of sin (x) in the graph above will also be multiplied by A. For the example shown in the OP, A = 1/2, which is why when x = π/2, y = (1/2) sin (π/2) = 1/2.

 

[JR Sauerland]

Using the "-" as a spacer is confusing, especially since "-" can indicate negation of a quantity or subtraction of two quantities.

If you want to clarify your math expressions, use parentheses " ( ) " or brackets " [ ] ". e.g. y = sin (x), rather than y = sin -x .

Now, as to your original question, for y = sin (x), y can have values between -1 and 1. Thus, the amplitude of the sine function is 1, as can be seen below:

​

If you multiply the sine function by a constant A, then all the values of sin (x) in the graph above will also be multiplied by A. For the example shown in the OP, A = 1/2, which is why when x = π/2, y = (1/2) sin (π/2) = 1/2.

I appreciate the clarification and the cool graph you made! I was just a little bit confused where they were drawing the values 0, 1, 0, -1, 0 from. It appears that they are multiplying the constant A by all of the values of the original amplitude, where the original amplitude is 1. However, the problem never specified it, so I guess it is implied. y=sin(x) is actually y=1sin(x) I suppose I could say, right? That is how the amplitude of y=sin(x) turns out to be 1, and goes from maximum of 1, to minimum of 1.

 

[SteamKing]

I appreciate the clarification and the cool graph you made! I was just a little bit confused where they were drawing the values 0, 1, 0, -1, 0 from. It appears that they are multiplying the constant A by all of the values of the original amplitude, where the original amplitude is 1. However, the problem never specified it, so I guess it is implied. y=sin(x) is actually y=1sin(x) I suppose I could say, right? That is how the amplitude of y=sin(x) turns out to be 1, and goes from maximum of 1, to minimum of 1.

These are some of the facts about the trig functions sine and cosine which should be learned very early when studying trigonometry. It should be obvious from studying a right triangle inscribed in a unit circle why the amplitude of the sine or cosine must be 1:

The diagram above shows the right triangle inscribed in the unit circle. As θ starts at 0 and goes to π/2, then π, 3π/2 and thence to 2π, it is clear that the value of sin(θ) takes on the values in the following table:

    θ            sin (θ)
    0               0
   π/2              1
    π               0
   3π/2            -1
   2π               0

As far as math expressions are concerned, such as y = x or y = sin (x), it is implied that 1 multiplies the RHS of each of these expressions. Any other multiplying factor must be written explicitly in the expression in order to be clear, such as y = 2x or y = 2 sin(x). For the latter, the factor 2 changes the radius of the circle from 1 to 2, and all the values of sin (x) are doubled as well.

This notation convention should be learned and thoroughly understood, otherwise your math education will be long and needlessly difficult.

 

[jedishrfu]

I would make a further suggestion that you checkout Khan Academy or MathIsPower4u.com for videos related to your question and see if they can clarify your confusion. In particular, I like how James Sousa handles math topics in a no nonsense to the point manner in a 10 minute video format.

Also as others have said treat your math studies very carefully. Remember every symbol used in math has a distinct meaning and to use them differently will create confusion in the long run. It would greatly if you learn about Latex and how to properly enter equations here. This skill will serve you later in college as you do your homework or projects and send it in my email to the professor.

 

[Mark44]

You need to spend more time looking at what is in front of you and less time posting here.

What are the "five key points", i.e. values of $x$, they are referring to? What are the values of $\sin x$ at each of these points?

You are extremely rude and disrespectful, not only to me, but to everyone else you reply to. I have actually spent the last week and a half reading my trigonometry book from cover to cover, 9 hours a day, and I'm on chapter 4. So you telling me to 'spend more time looking at what is in front of me' is a snarky, moot comment.

Given that you posted a problem that contains a graph of the relevant function, I am inclined to agree with @MrAnchovy's comment. If you are spending 9 hours a day on this stuff, it doesn't appear to be sinking in very well. It is one thing to read a mathematics text, but it is an entirely different thing to read it with understanding. The question you asked can be answered simply by looking at the graph and knowing a few values of the graphs of y = sin(x) and y = 2sin(x).

 

[JR Sauerland]

Given that you posted a problem that contains a graph of the relevant function, I am inclined to agree with @MrAnchovy's comment. If you are spending 9 hours a day on this stuff, it doesn't appear to be sinking in very well. It is one thing to read a mathematics text, but it is an entirely different thing to read it with understanding. The question you asked can be answered simply by looking at the graph and knowing a few values of the graphs of y = sin(x) and y = 2sin(x).

Have you seen his previous comments on my threads? He literally follows me around on the forums and posts rude and harassing stuff. If that's the type of environment you condone on this site, I will leave Physics Forums and go elsewhere. I thought this was a place for people who needed help that are making an honest effort. In my opinion, it's not treating me very fairly for you to say "...can be answered simply by looking at the graph and knowing a few values of the graphs of y = sin(x) and y = 2sin(x)."

Sometimes, it just doesn't work like that. Sometimes, students can't just look at a problem or a graph and get it like everyone else can. Is shamming me or basically implying that I'm not as skilled at math or as good as math supposed to help me any, like really?

 

[Mark44]

Given that you posted a problem that contains a graph of the relevant function, I am inclined to agree with @MrAnchovy's comment. If you are spending 9 hours a day on this stuff, it doesn't appear to be sinking in very well. It is one thing to read a mathematics text, but it is an entirely different thing to read it with understanding. The question you asked can be answered simply by looking at the graph and knowing a few values of the graphs of y = sin(x) and y = 2sin(x).

Have you seen his previous comments on my threads? He literally follows me around on the forums and posts rude and harassing stuff. If that's the type of environment you condone on this site, I will leave Physics Forums and go elsewhere.

No, I haven't seen Mr Anchovy's previous comments, in part because I was out of the country for two weeks. If you feel that someone is being rude, use the Report button and a mentor will take a look.

I thought this was a place for people who needed help that are making an honest effort. In my opinion, it's not treating me very fairly for you to say "...can be answered simply by looking at the graph and knowing a few values of the graphs of y = sin(x) and y = 2sin(x)."

IMO you are being overly sensitive here. Based on the problem you posted, it's not unreasonable for us to expect that you already have some knowledge about the graphs of y = sin(x) and y = 2sin(x), such as the x-intercepts and maximum and minimum values. The study of mathematics is very sequential, so if there is some concept that you're not getting at one point, it will likely come back around sometime later and cause you problems. My remark about you spending 9 hours a day is related to this. Speed-reading is generally not a good strategy for studying mathematics, and as well, it takes time for some concepts to gell in your mind.

A better strategy is to read a short section and then work lots of problems in that section to see if you're getting it.

Sometimes, it just doesn't work like that. Sometimes, students can't just look at a problem or a graph and get it like everyone else can.

Why not? Being able to see the information that is conveyed in a graph is a basic skill. If you haven't developed this skill, do some practice problems until you get better at it, but don't just keep plowing ahead.

Is shamming me or basically implying that I'm not as skilled at math or as good as math supposed to help me any, like really?

 

[micromass]

Have you seen his previous comments on my threads? He literally follows me around on the forums and posts rude and harassing stuff. If that's the type of environment you condone on this site, I will leave Physics Forums and go elsewhere. I thought this was a place for people who needed help that are making an honest effort. In my opinion, it's not treating me very fairly for you to say "...can be answered simply by looking at the graph and knowing a few values of the graphs of y = sin(x) and y = 2sin(x)."

Sometimes, it just doesn't work like that. Sometimes, students can't just look at a problem or a graph and get it like everyone else can. Is shamming me or basically implying that I'm not as skilled at math or as good as math supposed to help me any, like really?

Ok, but then I think it's clear you're doing something wrong. That you are not able to answer your own question "simply by looking at the graph" is nothing to be ashamd about of course, but it does mean that you are missing a certain type of foundational knowledge. You cannot expect to understand trig without already knowing how graphs work. I think you need to start all the way from the very foundations and work up from there. Because -I promise that I'm not trying to be rude- but somebody who cannot answer the question in your OP, such a person is not ready for trig. You need to have a long hard look at what you currently know math-wise, and what you don't know. We can help you with this. Or even better, take a look at the ALEKS system, it has a brilliant way of gauging what level a student is at. https://www.aleks.com

And no, speedreading math is not a good option. I would be very interested in knowing precisely how you approach studying mathematics. In my experience, studying mathematics is a very very slow process. There are not many occasions where I can advance more than 5 pages in a given book in a given day. (Sure, I can do more, but I have noticed over and over again that this will come back to haunt me later on because I don't grasp the material as well as I should). Furthermore, one should spend most of their time doing problems. So for every page or concept you read, you should do a substantial amount of problems. This is the only way to do math.