Further Mathematics 7367: Trigonometry Topical Past Paper Questions

The function f is defined by $$ \mathrm{f}\left(x\right)=\left|\sin x+\frac{1}{2}\right|\qquad(0\leq x\leq2\pi) $$ Find the set of values of x for which $$ \mathrm{f}(x)\geq\frac{1}{2} $$ Give your answer in set notation. [5 marks]

Two of the solutions to the equation $ \cos 6\theta = 0 $ are $ \theta = \frac{\pi}{4} $ and $ \theta = \frac{3\pi}{4} $. Find the other solution to the equation $ \cos 6\theta = 0 $ for $ 0 \leq \theta \leq \pi $. [2 marks] (b) Use de Moivre's theorem to show that $ \cos 6\theta…

(a) Given that $$ \sinh\left(A+B\right)=\sinh A\cosh B+\cosh A\sinh B $$ express $ \sinh(m+1)x $ and $ \sinh(m-1)x $ in terms of $ \sinh mx $, $ \cosh mx $, $ \sinh x $ and $ \cosh x $ [1 mark] (b) Hence find the sum of the series $$ C_{n}=\cosh x+\cosh2x+\cdots+\cosh nx $$ in te…