Mathematics Pure WMA11: Trigonometry Topical Past Paper Questions

Figure 3 The curve C, shown in Figure 3, has parametric equations $$ x=6\sin t\quad y=5\sin2t\quad0\leqslant t\leqslant k $$ where k is a constant. The region R, also shown in Figure 3, is bounded by C and the x-axis. This region is rotated through $ 2\pi $ radians about the x-ax…

Figure 2 Figure 2 shows a sketch of the curve C with equation $$ x=\frac{2}{3}\sin\left(3y+\frac{\pi}{4}\right)\qquad\frac{\pi}{12} (3) (b) Show that $$ \left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^{2}=\frac{1}{p-q x^{2}} $$ where p and q are integers to be found. (4) The normal…

Figure 3 The curve C, shown in Figure 3, has equation $$ y=\frac{x^{-\frac{1}{4}}}{\sqrt{1+x}\left(\arctan\sqrt{x}\right)} $$ The region R, shown shaded in Figure 3, is bounded by C, the line with equation x = 3, the x-axis and the line with equation $ x = \frac{1}{3} $ The regio…