Cosine is the derivative of sine.
y = sin(x) - Domain: D = ℝ, x, x0, x<> x0 in ℝ, Δx = x − x0, Δy = f(x)-f(x0).
[sin(x)] ’ = f’(x) = lim (Δy/Δx) = lim [f(x0+Δx)-f(x0)]/Δx = cos(x)
The derivative of sine, y = sin(x) —by its conceptual definition as “slope of the tangent line”— is change-in-y-over-change-in-x = dy/dx = -sin(x)/1 = -sin(x)
Likewise, the derivative of sine is = cos.
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Just decided to take a nap with my boyfriend over skype (dont judge) and 20 minutes accidentally turned into 2 hours oops
Vincent van Gogh (March 30, 1853 – July 29, 1890)
I haven’t got it yet, but I’m hunting it and fighting for it, I want something serious, something fresh—something with soul in it! Onward, onward.
one time when my dad was in college these guys found a carpet on the sidewalk and they needed furniture for their dorm so they were like “hell yeah free carpet” and they carried the carpet upstairs and it was really wet and heavy so they unrolled it to let it dry and a dead body fell out
I’M NOT SHITTING YOU
Confused husky pup
He’s not expressing confusion, he’s tilting his head for better sound localization. While having an ear on each side of the head is good for lateral echolocation, tilting the head so that the ears are offset gives it vertical depth.
Oh my gosh, that explains why some dogs put their head to one side when you talk to them. They’re not confused, they’re trying to listen to us better. Awww.
"Spilled my heart here"
I saw this on my walk today and it broke my heart..
"I don’t understand bisexuality, I don’t think it exists"
well I don’t understand physics but you don’t see me floating off into space because gravity no longer applies to me
“I hope I can say this without offending anybody, but imagine a baseball inside of a clear basketball”
This is how the solar system is actually moving as it traverses the galaxy.
We are GROOT!