Further Pure Math 9-1 4PM1: Trigonometry Topical Past Paper Questions

Figure 4 Figure 4 shows a right pyramid ABCDE with • vertex $E$ • horizontal square base ABCD of side 6 cm $ \cdot \quad EA = EB = EC = ED = 12 \, cm $ • vertical height of $h$ cm (a) Show that $ h=3\sqrt{14} $ (3) (b) Find, in degrees to one decimal place, the size of the angle…

(a) Using a formula given on page 2, show that $$ \cos2\theta=2\cos^{2}\theta-1 $$ (b) Hence show that $$ \int_{\frac{\pi}{3}}^{\frac{3\pi}{4}}\left(2\cos^{2}\theta-1\right)\mathrm{d}\theta=-\frac{a+\sqrt{b}}{c} $$ where $a$, $b$ and $c$ are integers to be found. (4) Diagram NOT…

(a) Use a formula on page 2 to show that $ \sin^{2}A=\frac{1}{2}(1-\cos2A) $ (3) (b) Show that $ \sin^{4}x + \cos^{4}x = \frac{3 + \cos 4x}{4} $ (5) (c) Hence solve, in degrees to one decimal place, the equation $$ 8\sin^{4}\left(\frac{\theta}{2}\right)+8\cos^{4}\left(\frac{\thet…