Mathematics Pure Math 1 9709: TRIGONOMETRY Topical Past Paper Questions

(a) The first term of an arithmetic progression is 5730 and the common difference is -23. Find the value of the first negative term. (b) The first term of a geometric progression is $ \sin\theta $ and the second term is $ \frac{1}{2}\tan\theta $, where $ 0 < \theta < \frac{1}{2}\…

(a) Show that the equation $$ 6\sin\theta+\frac{1}{\tan\theta}=\frac{4}{\sin\theta} $$ can be written in the form $$ 6\cos^{2}\theta-\cos\theta-2=0. $$ (b) Hence, solve the equation $$ 6\sin\theta+\frac{1}{\tan\theta}=\frac{4}{\sin\theta} $$ for $ 0^{\circ} \leq \theta \leq 360^{…

$$ \mathrm{S o l v e t h e~e q u a t i o n}4\sin^{4}\theta+12\sin^{2}\theta-7=0\mathrm{f o r}0^{\circ}\leqslant\theta\leqslant360^{\circ}. $$