from Rodrigues' formula we know that : $$K^{2}\left ( 1 - \cos\varphi \right ) + K \sin{ \varphi} + I = R$$ we also know that $K$ should be $$K =\fra...

I'm trying to self-study Differential Forms in Algebraic Topology by Bott and Tu. I've come across this exercise: Show that the closed Poincare ...

$$\int {\sin \theta + \cos \theta \over \sqrt{\sin 2\theta} }d\theta$$ After simplifying I get, $${1\over \sqrt{2}}\int {\tan \theta + 1 \over \sqrt{\tan ...

$\sin^{4}x+\cos^{4}x$ I should rewrite this expression into a new form to plot the function. \begin{align} & = (\sin^2x)(\sin^2x) - (\cos^2x)(\cos^2x)...

$v(x)$ given $a(x)$, where $v_0 = 0$ and $x_0 = 0$ I'm clueless. This is what I thought: $dv = v, dx = x$ $a(x) = \frac{dv}{dt} \frac{dx}{dx} = \frac...

There is this incredible glass figure on the front of my Calculus textbook, I searched online for what this figure is called and the formula for creating ...

I am having trouble seeing the difference between weak and strong induction. There are a few examples in which we can see the difference, such as reaching...

I am trying to understand why $$\sin(4\pi/5) = \sin(\pi/5)$$ Is there any formula that could help me? Thank you

What is the value of $1^i$? $\,$

From my understanding these two statements are logically equivalent p → q ≡∼p ∨ q (can someone 'explainlikei'mfive' why that makes sense) W...