Prove that $\cot^2{(\pi/7)} + \cot^2{(2\pi/7)} + \cot^2{(3\pi/7)} = 5$ . I am sure this is derived from using roots of unity and Euler's complex numb...

consider the following situation of a double pendulum. We found the moving equations as $$ \ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\...

Same Mom trying to help daughter here. Once I know how to explain this pattern, can you tell me what I'd call this area of math so I can go re-teach ...

I've started reading All of Statistics by Larry Wasserman with the hope of gaining understanding of machine learning fundamentals. The author gives t...

I am having difficulty finding parametric equations of the curve of intersection of $z = x^2 - y^2$ and cylinder $x^2 + y^2 = 1$ I am aware that the first...

Context I am an undergrad student taking Abstract Algebra I, and this is a problem on a homework assignment. Problem Let $H$ be a normal subgroup of $G$, ...

Let $u = \arctan(x)$, hence $x = \tan(u)$ for $u$ belongs in $(-\frac\pi2, \frac\pi2)$. Since $u$ belongs in $(-\frac\pi2, \frac\pi2)$, we consider $\sin(...

Given a 3-variable right-handed vector v that is a translation measured in local space and a unit quaternion representing an orientation from local to wor...

Can someone please help me with the 3 calculus one word problems below, I've done all three of them several times but can never seem to arrive at the...

edit I updated my question at the end, I think the claim may be false? Let $(L,\lambda)$ be a limit cone of a diagram $D$ in a category. For any object $X...