Proving The Identity: Prologue
Prove the identity: (sine2x/ sine x)-(cosine2x/ cosine x) =secant x.
… I can use a double angle identity for both sine2x and cosine2x. Sine2x equals (2sin x)(cos x), and cos2x
can equals (1-2sin^2x)… Then I can simplify them even further and see if the right side equals the left…
We see Arme working diligently on her trigonometry homework. She slouches in her seat with a hefty textbook on her lap and a spiral bound notebook in her hands. Arme scribbles onto her notebook feverishly, but in seconds her pencil hits the ground and her hands go to her heart shaped face.
She is tired; very, very tired.
It is nearly midnight, yet she still has much to do. She massages her temples and her hands become snarled in a tangled purple mess, her hair. Her violet irises are surrounded by swollen, puffy red, barely contained by her eyelids. Her ragged eyes are complete with dark circles. She truly looks hideous, with her worn out features, her frail frame, and her pasty skin. Others avoid her for it.
She's lonely, she's perfectly friendly and she wants to have more friends, but she ends up nearly as a social pariah. It's all because of her terrible appearance, but she knows she can't spend any time fixing herself up. How long has it been since she was able to focus on vanity, on anything? She just doesn't have the time anymore.
But she's only 16, a senior at a reasonably prestigious high school, although that's not the problem. More than advanced, she was able to skip two levels of her education: preschool and then the last year of junior high. She still does very well in her studies, although small slipups make themselves apparent every once in a while.
Lately, however, her grades have been dropping.
She used to be ranked at second place for the senior class. Now she's at seventh. Arme once dreamed of graduating as the Valedictorian for her class and moving on to a university for medical studies. But now she is further away from her goal. Graduating at the top plaintively isn't her destiny. Becoming known for her talents obviously isn't her fate. Becoming somebody important, becoming somebody known isn't going to be her future. Her destiny must be to lead a miserable, unimportant life, what she resents the most.
She's too exhausted to get up, but she does so anyway. She retrieves the fallen pencil and gets back to work, despite the sharp pain that clouds her mind. She tells herself that it'll all be over soon.
That's what keeps her sane. Her optimism.
Not more than two years ago, she had lost grip of her positive outlook and walked a path of self-mutilation and self-loathing. Her parents had fussed over her after discovering the change in her attitude, and it was clear that they were severely worried.
But it was also clear that they didn't know what she was going through. Nobody did. Arme liked to believe that her chronic depression was justified, but outsiders and other students who knew nothing about her thought that she was being overly dramatic. They were simply judgmental, and it was even worse that she had no chance of explaining.
She was the center of many's gossip. She didn't want to be known this way.
She had hated every moment of it. She still does, but showing it wouldn't solve much.
Soon Arme finishes her work. It has taken a mere hour, but every hour is important for this one girl. Too important. Simply fatigued, Arme can't help but plop onto her slovenly-made bed. She doesn't have the energy to take a bath, nor brush her teeth or even eat. She's used to the hunger; she's used to her parent's divorce.
But she's not used to the major difference between her and everyone else.
In her final moments before she descends into slumber, her optimism fades. But just for a moment.
She quickly curses many things. She curses the rift that has formed between her parents. She curses her haggard appearance. She curses all the ignorant outsiders that added difficulty to her life. And last but not least…
…She curses her own need to transition through worlds.
End Of Prologue
Hey guys, thanks for taking a look at my first Grand Chase fanfiction. It seems so far that Arme has a few psychological issues. For one, she acts almost desensitized, but she's not going to stay emo forever. She's not going to look repulsive forever, either. The rest of the story will be written in past progressive, or whatever you call it, rather than present progressive, also.
Just so you know, I'm not trying to make her a mary-sue. No, she's not going to be an empty shell, she's not going be the sexiest chick on the planet, she's not going to score all the hot dudes, and she's not going to be the strongest character ever. No. Just no. I'm going to make her more of a real character, rather than a pair of pants that somebody can put on and wear, and pretend that they're her. If I was going to, then I'd just name her "Pants".
It might seem boring right now, but I promise that it will become more interesting. I might even add some romance, if you please. The genre, for now, it will be supernatural. I don't think romance will come too soon, and the whole story won't be revolving around it either, so I probably won't be listing that as one of the genres. Maybe mystery, adventure, or so on will be the other genres.
Until I update, send some reviews my way! What should I change, what should I add, do you like it, do you hate it… Just tell me so I can make this story better.