For all of her life, cos(x) wanted to be known as more than just a cosine; than a standard function. She’d seen her friends and family accept that, solving trigonometric equations mostly, with some occasional dabbling in the realm of fields.

It was like they were stooping to the level of the sines, the basic and bland functions which were a black mark upon functional society as a whole. They were all so boring; so mundane, and her fellow cosines seemed content in wallowing amidst the filth.

None of that was for her; she wanted to shoot for the stars. She wanted to be used in the realm of engineering; of Fourier analysis. The young function dreamed of it day and night, eagerly awaiting the time in which she would be called upon.

Then she’d found it: her chance to be derivative. It was a textbook on Simple Harmonic Motion, a thick manuscript in desperate needing of her help. She’d signed on immediately of course, gaining a derivative notation with pride.

Her family had warned her that nothing good could come of it; that she should take things easier and enter a middle school math book instead. But she ignored them. She was cos(x)dx now, and there was nothing anyone could say about it!

Or so she had thought.

Cos(x)dx was relaxing on her page when a loud shriek broke her silent reverie. She looked across its script-laden vastness to find her neighbor csc(x)dx panicking. That wasn’t like the cosecant, who cos(x) had privately viewed as a big sister.

“W-what’s wrong?” She called, watching as a strange shape approached the function on the horizon. It looked almost like a tilde on its side, vertical squiggle that filled her x with dread.

“It’s ∫! It’s come for me; for us!” Csc(x)dx wailed, the symbol now ever-so-close to her.

Then, before cos(x)dx could respond, it was upon her friend, changing her; splitting her. Cos(x)dx’s eyes widened as the function shrieked, splitting into two forms; her derivative notation shoved aside by the encroaching ∫. One looked like herself; but the other… It was a cotangent, wild and bestial.

Csc(x) screamed as the cot(x) snapped at her, the function rabid. Then, before she could so much as run, a massive logarithm bounded them, surrounding them with negative energy that froze them fast.

No longer was she the strong and proud csc(x)dx that cos(x)dx had looked up to. Now she was a quivering mess, bounded by a prison and held together with a savage: -ln|csc(x)+cot(x)|+C. The plus C was added on at the end, some irrelevant notation to express a concept cos(x)dx didn’t quite understand.

But she had a feeling she’d know soon enough, the appearance of another ∫ heralding changes of her own. She felt it coming before she saw it, a foreboding sensation gripping her upper and lower bounds.

“N-no!” She whimpered, the sound like the frightened squeak of an inverted tangent. “I… I don’t want to be changed!”

It was like she was shouting into an empty plane, and she whimpered as the awful ∫ fell upon her, her form unraveling at its behest.

Her x thumped hard in her parentheses as she felt her curves begin to change, translating horizontally. Desperately, she tried to clutch to the y-axis, but her hold was slipping, being pulled from one to zero.

Her x sank as she realized what she was becoming, and despair filled her. “No, I don’t want to be a sin! Anything but that!”

Cos(x)dx tried to fight harder, but already her derivative notation was slipping away, stripping her bare until she was just a cosine again. Then her form locked into place, crossing the x axis at even intervals of pi rather than meeting it halfway like she was used to.

She was… Was she even a she anymore? No, that couldn’t be the case. He was sin(x) now, a sine function condemned to live the life of stagnation that a young cosine function had once dreaded.

Despite the ever-fading protests in his wave, sin(x) felt calm. It was not within his capacity to dream; to be anything more than he was. The vapid mentality of a basic function finally registered across his wave, and he enjoyed it.

He was a sine now; just a sine and nothing more than one.

The soul of a rebellious, derivative cosine faded away, eradicated as though they’d been rubbed out by an eraser.

He could still remember who he was; something which occupied his every thought. It was his purpose, to convey his message to the world. A quiet C drifted towards the edge of his parentheses, and he accepted it gratefully.

“∫cos(x)dx=sin(x)+C”

He said it quietly at first, then louder and prouder the next time. This was him; this was all he was.

“∫cos(x)dx=sin(x)+C”