The diagram shows the curve with parametric equations $$\[ x=4 t+\mathrm{e}^{2 t}, \quad y=6 t \sin 2 t, \]$$ for $$$0 \leqslant t \leqslant 1$$$. The point $$$P$$$ on the curve has parameter $$$p$$$ and $$$y$$$-coordinate 3 . Show by calculation that the value of $$$p$$$ lies between $$$0.5$$$ and $$$0.6$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_22 Year：2021 Question No：7(b)

Answer:

Consider sign of $p-\frac{1}{2 \sin 2 p}$ or equivalent for $0.5$ and $0.6$
Obtain $-0.09 \ldots$ and $0.06 \ldots$ or equivalents and justify conclusion

Knowledge points:

2.6.1 locate approximately a root of an equation, by means of graphical considerations and/or searching for a sign change

Answer:

Knowledge points:

Solution:

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