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![stay for the actual edit, trust || #aot #aotseason4 #floch #yeagerist #targetaudiance || Happy birthday to Floch. Paradis' Hero || The Yeagerists (イェーガー派 Yēgā-ha?) were the ruling faction of Eldia on Paradis Island that came into existence in 854. They were a former rebel faction supported by civilians and soldiers from the military secretly gathered by Floch Forster. Their initial goal was to reunite Eren Yeager with his half-brother Zeke,[3] in order to ultimately assist the former in the activation of the Rumbling. As a militant ultranationalist faction, they fought for the sake of the ensuring the Eldian people's survival on Paradis, exhibiting a disdain towards the anti-Eldian peoples of the outside world such as the Marleyans, and believing the Subjects of Ymir to be a superior race, they also wished to create the New Eldian Empire with Eren leading it as the Founding Titan.[4] In the month following the Raid on Liberio, the Yeagerists conducted a military coup and took power within the Walls, officializing their complete control over the island of Paradis a couple days after the start of the Rumbling. By the year 857, the Yeagerists were reformed and merged into the Eldian Army, with the objective of protecting Eldia from the threats of retaliation from surviving nations after Eren Yeager's death during the Battle of Heaven and Earth.[5]](/video/cover/7694135562676079894.webp)
![Sine turns into cosine. So why does cosine turn into NEGATIVE sine? Who invited the minus sign? 😭 I thought we were just swapping the names. Apparently we have to look at the actual graph. Annoying. Fair. The derivative tells us the slope: how steeply the original graph is going up or down at each position. Now watch cosine from x = 0 to π. It starts at the top, falls through zero, and reaches the bottom. Between those endpoints, it's going DOWN. But sine is above zero for that whole stretch. If ordinary sine were the derivative, it would be reporting a positive slope. It would be telling us we're going uphill while we're visibly walking downhill. Wrong sign. S-I-G-N. The other one. Look at the shape of the slope instead: At x = 0: flat, so slope 0. At x = π/2: steepest downhill, so slope −1. At x = π: flat again, so slope 0. 0 → −1 → 0. That's the sine hump flipped upside down. Negative sine. Then cosine starts climbing from π to 2π. We need positive slopes now. Sine is below zero there, so flipping it makes its values positive. The same minus sign fixes the entire climb. With x in radians: d/dx [cos(x)] = −sin(x) And then I made the mistake of asking what happens if we KEEP taking derivatives. sin(x) → cos(x) → −sin(x) → −cos(x) → sin(x) Each arrow means “take the derivative.” Four steps and we're back where we started. Calculus has put us on a very small roundabout. Why does the last step work? The derivative of cos(x) is −sin(x). The extra minus in −cos(x) flips that result, giving −(−sin(x)) = sin(x). Two things to keep separate: a graph's height and its slope. At x = π/2, cosine has height 0 but slope −1. Crossing the axis doesn't mean the graph is flat. A slope of −1 means a tiny step right gives roughly the same-sized drop in height. It's a rate of change, not a height. This cycle belongs to these sine and cosine functions; it isn't a rule for every graph. And radians matter for the formulas written here. Save this for the next time that minus sign looks like it appeared from nowhere. What would the FIFTH derivative of sine be? Textbook: OpenStax, Calculus Vol. 1, §3.5. #Calculus #Trigonometry #MathExplained #GravityAssist](/video/cover/7700309341051604237.webp)
