## Statistics

##### Anime Stats

Days: 43.1

Mean Score: 7.88

- Total Entries205
- Rewatched0
- Episodes2,382

##### Manga Stats

Days: 5.6

Mean Score: 8.18

- Total Entries16
- Reread0
- Chapters958
- Volumes111

Days: 43.1

Mean Score: 7.88

- Total Entries205
- Rewatched0
- Episodes2,382

Days: 5.6

Mean Score: 8.18

- Total Entries16
- Reread0
- Chapters958
- Volumes111

## All Comments (256) Comments

•●•MAL Book Club•●•renascence

[spoiler]

We are proud to deliver to you our very first Newsletter. The Club has been brought back to life for about four months now and we plan to make many things in the future for all the members to enjoy. For now here are some of the things that may interest you.

Read TogetherIf you are interested in reading with someone else in the club, either by choosing from those who have their names and reading choices listed, or by joining the list, you can visit the above link.

Mini Event: Anime & LiteratureWe will hold an anime-watching event throughout May, and currently we are opening a poll for you to vote for the anime that will be included in the event. Visit the given link for more information and also to cast your vote. The poll will be open for approximately one week.

Other threads to join:Introduce yourself (if you haven't)

Ask for reading recommendation

Brag about books you currently read

...or just completed

General discussion

News of literary world

Our GamesGuess the characters

Biblio This or That

Anagram: Harry Potter Edition

Useful links:Forum rules & guideline

Table of content

The staffs

Staff Recruitment:

OpenIf you would like to receive more Newsletter in the future, you can

subscribe here.We look forward to seeing you at the club!!!And this is a dumb question but do you want to listen to a song I composed and produced? I'm pretty drunk right now but it would humor me for you to listen to it, if you don't want to no prob lol:

http://sheepdude.bemaniso.ws/Brandon%20Scott%20Williams%20-%20In%20Your%20Element.mp3

But anyway if you wanna listen to an amazing song try Ulrich Schnauss - A Letter From Home. Always nice to broaden your horizons, right?

its from Toaru Majutsu no Index

Delete

KumaHunter | Yesterday, 10:11 PM

what's the anime on the "100 members" banner?

If you need more explanation than that, get back to me.

Yeah I've used it but only a small bit. Depends what you're using it for, it does a lot of stuff.

-The amplitude is the vertical distance from the center of the sine wave to one of its peaks or troughs.

-The "center" is the line which runs through the middle of the graph.

-The period is the distance from one peak to another or from one trough to another.

-The phase shift is the distance that the graph is shifted left or right. Notice that the phase shift is modular, meaning if you shift the graph by a multiple of its period, you essentially get the same graph.

Here's the general form of the sine equation:

f(x) = a sin(bx - h) + k

Let's take the most basic form of the sine equation and compare it to the general form in order to examine these values:

f(x) = sin(x)

We know that sin(x) varies between -1 and 1. The amplitude is the distance from the center of the wave (the line y = 0 in this case) to any peak or trough, which in this case is obviously 1. The general way of solving for the amplitude algebraically is to find the distance between the highest point and lowest point on the wave and divide by 2. This gives:

amplitude = a = (maximum value - minimum value)/2 = (1 - [-1])/2 = 2/2 = 1

The center is simply the line that lies on the midpoint between the highest and lowest points. If you recall, the midpoint on a line between two points p and o is (p+o)/2. So:

center = k = (maximum value + minimum value)/2 = (1 + [-1])/2 = 0/2 = 0

The center for our given equation is y = 0, which is what we would expect.

You can also examine the effects of b and h on the graph if you wanted. b effectively shrinks or expands the graph horizontally by changing the length of the period, and h affects the starting point of the wave. I don't have a solid approach for examining the sine equation since my knowledge has come from experimentation and deduction, so excuse me if my explanation isn't coherent enough. I doubt you'll need to do this sort of thing on any calculus test, anyway.

June 20 is the 171st day of the year.

December 21 is the 355th day of the year.

If we take f(x) to be the function representing the length of daylight on a given day x, 0<x<366, then we have:

f(171) = 14 hours, 32 minutes, 47 seconds = 14.55 hours

f(355) = 9 hours, 46 minutes, 13 seconds = 9.77 hours

Due to the cyclic nature of the rate of change of daylight, we choose sine to be our representative function. The general form of the sine equation is:

f(x) = y = a sin(b[x - h/b]) + k

a is the amplitude

b is the frequency

h affects the phase shift

k is the center of the amplitude

All these values are fairly simple for us to find if we understand exactly how they modify the sine function.

a = (maximum value - minimum value)/2 = (14.55 - 9.77)/2 = 2.39

b = 2 pi / period = 2 pi / 365

k = (maximum value + minimum value)/2 = (14.55 + 9.77)/2 = 12.16

h/b is a little trickier to figure out. Normally, the highest point on the sine graph occurs a quarter of the way through the period (x = 365/4 = 91.25 in our case) but we want it to occur at x = 171, so we need to move the graph 171 - 91.25 = 79.75 units. Therefore, we set h/b = 79.25.

The resulting equation is:

f(x) = y = 2.39 sin([2 pi/365][x - 79.25]) + 12.16

Simplify to get:

f(x) = 2.39 sin(2 pi x/365 - 158.5 pi/365) + 12.16

The graph isn't perfect but it's damn close (remember in the previous problem I said we must assume a perfect system? Unfortunately, a function of the amount of daylight in a day isn't a perfect sine wave). The only thing that's really difficult about this problem is knowing what the constants in the sine equation are and how to use them to manipulate the graph.