Cambridge Maths Academy

수학 모음 (Maths collection) 전체보기 1. Area of a regular octagon Question. Find the area of a regular octagon with side length $a$. (4-9 Higher GCSE by Michael White, Ch13 Geometry 4, p.426 Q19.) We consider the area of the triangle with an angle $\theta$ subtended at the centre. $$ \begin{align} \theta=\frac{360}{8}=45^\circ \end{align} $$ The height $h$ of the triangle is given by $$ \begin{align} \..

수학 모음 (Maths collection) 전체보기 This question comes from a test paper for A-level maths for Michaelmas Term at Eton College. Q15. (a) Express $\cos(2\theta)+\sin(2\theta)$ in the form $R\sin(2\theta+\alpha)$ where $R>0$ and $0 < \alpha < \frac{\pi}{2}$. [3 marks] (b) Hence show that $$ \begin{align} \frac{1-\sqrt{2}}{2}\le \cos\theta(\cos\theta+\sin\theta) \le\frac{1+\sqrt{2}}{2} \end{align} $$ fo..