Math >.>

[3823]

I've been staring at this problem for 30 minutes and I keep getting it wrong and the answers explaining why aren't helping. .-.

I know in an equation you're supposed to use 2pi/4 to get the period but idk how to do it here.





Answers:

Spoiler

I don't understand why we are subtracting those two numbers and where the 2 came from
I'd appreciate it if someone could help c:

It's probably something really obvious but ima move on from now and get back to it later. >.<

 

[Luna]

Allow me, an aspiring polymath organic chemist who trains in the art of autodidact, to help.

First, we deconstruct this mathy conundrum. According to the question, they request the period of the function (presumably a sine/cosine function it seems). The answer sheet you provided seems to precede what you should have learned before encountering the problem, so I'll use it for reference. The graph shows that a period is measured from one inflection point on the rising edge of the graph to another succeeding inflection point on, yet again, a rising edge.

In addition, the points used to measure the period have the same y-value of -7. This means we focus on the x-coordinates. We start by remembering how to find the length between two points in regards to a number line. Suppose the coordinates were (5, 10) and (8, 10). Without math, we can determine that the length between the two points is 3. But mathematically, we found out using the expression 8 - 5. Essentially, since the y-coordinates are the same in this problem, so we perform the same operation. Thus, it is

π - (- 2/3 π)

We got π from (π, -7) and negative 2/3 π from (-2/3π, -7). We placed them in the order that they appear in the graph.

Evaluating the expression, we get 5/3 π. That is the length between the two specified points of the function.

Since, logically, we know what makes a period, we just double that result to achieve 10/3 π, which is where the two comes from.

Does that make sense?

 

[3823]

Thanks ^-^

π - (- 2/3 π)

Why did you subtract them?

 

[Luna]

Why did you subtract them?

The reason for subtracting them stems from the fact that this is the method for finding the distance between two points on a number line, since in the problem, the y-coordinates are the same, so you treat the graph like a number line as you are simply finding the period.

Here is an example so that you can have a conceptual understanding of what I'm saying rather than following blind rules.

The distance between point A and point C is five, an objective observation. (Ignore point B, Google images blows hard.)

You determine this by getting 3 and subtracting -2, which is the method for finding a distance between two points within a common elevation. That is what we apply to the problem with its own coordinates to find the period...

Does that make sense? Sorry if my explanations are superfluous or lack thereof, I struggle to help others in math without being there in person.

 

[3823]

The reason for subtracting them stems from the fact that this is the method for finding the distance between two points on a number line, since in the problem, the y-coordinates are the same, so you treat the graph like a number line as you are simply finding the period.

Here is an example so that you can have a conceptual understanding of what I'm saying rather than following blind rules.

The distance between point A and point C is five, an objective observation. (Ignore point B, Google images blows hard.)

You determine this by getting 3 and subtracting -2, which is the method for finding a distance between two points within a common elevation. That is what we apply to the problem with its own coordinates to find the period...

Does that make sense? Sorry if my explanations are superfluous or lack thereof, I struggle to help others in math without being there in person.

I get it! :3

Why did you multiply by 2 tho?

 

[Luna]

Why did you multiply by 2 tho?

*Pant pant*

Ok, so we multiply by two because once we found the distance between the two points, that constituted only half of the period.

Another example for cementing conceptual understandings on such an idea-based subject.

What we calculated on your graph equates to finding the distance between 0 and π on this graph. However, the period is represented by the distance between 0 and 2π. Instead of calculating the distance between π and 2π and adding it to that of 0 and π, we just multiply the distance we found between 0 and π by two because the distance is the same nonetheless. This gives us the period.

Does that make sense?

 

[3823]

Does that make sense?

Yes.

So the two loops equal one cycle, which is the period right?

 

[Luna]

So the two loops equal one cycle, which is the period right?

Indubitably. Although I wouldn't call them cycles, should you ever pursue Digital Electronics, as it will get very confusing.

If this concludes my help, may you rate me? It is important for me to be self-aware of my abilities to contribute help aimed towards others.

 

[3823]

Indubitably. Although I wouldn't call them cycles, should you ever pursue Digital Electronics, as it will get very confusing.

If this concludes my help, may you rate me? It is important for me to be self-aware of my abilities to contribute help aimed towards others.

You helped a lot. The pictures were really useful too. Thankyou c: