The curve $y=3\cos\left(x-\dfrac{\pi}{3}\right)$ meets the $y$-axis at $P$ and first meets the

Question

The curve $y=3\cos\left(x-\dfrac{\pi}{3}\right)$ meets the $y$-axis at $P$ and first meets the positive $x$-axis at $Q(b,\ 0)$. The chord $PQ$ is drawn. Find the exact value of $b$.[2] Find the equation of the chord $PQ$.[2] Hence find the exact area enclosed by the curve and the chord.[5]

Accepted Answer

(i) $b=\dfrac{5\pi}{6}$ (ii) $y=\dfrac32-\dfrac{9x}{5\pi}$ (iii) $3+\dfrac{3\sqrt3}{2}-\dfrac{5\pi}{8}\text{ units}^2$

Shifted cosine curve and its chord

Shifted cosine curve and its chord

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