Cambridge Maths Academy

수학 모음 (Maths collection) 전체보기 Question. Find $\frac{dy}{dx}$ for: $$ \begin{align} \textrm{(a)}&\qquad y = \arcsin(1-2x) \\ \textrm{(b)}&\qquad y = \arctan\left(x^2+1\right) \end{align} $$ Solution. (a) For $y=\arcsin(1-2x)$, we have $$ \begin{gather} -1\le 1-2x \le 1 \\ -\frac{\pi}{2}\le y \le\frac{\pi}{2} \end{gather} $$ We re-express the equation $$ \begin{align} y&=\arcsin(1-2x) \\ \Rightarr..

수학 모음 (Maths collection) 전체보기 Heron's formula calculates the area of a triangle. Here, we will look at two different formulae describing the area of a triangle and then derive the third version, Heron's formula. $A=\frac12ah$ $A=\frac12ab\sin C$ Heron's formula: $A=\sqrt{s(s-a)(s-b)(s-c)}\,$ where $s=\frac{a+b+c}{2}$. s can be thought of as half the perimeter of the triangle. As we will see, the..