Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

A curve is defined by the equation $y = 2\cos x$.
(i)[2]

Sketch the graph of $y = 2\cos x$ for $-\pi \leq x \leq \pi$, and state the coordinates of the point where it crosses the $y$-axis.

(ii)[2]

Points $P$ and $Q$ lie on the curve, with $x$-coordinates $\frac{1}{3}\pi$ and $\pi$ respectively. Find the length of $PQ$ correct to 1 decimal place.

(iii)[3]

The line through $P$ and $Q$ cuts the $x$-axis at $H\,(h, 0)$ and the $y$-axis at $K\,(0, k)$. Show that $h = \frac{5}{9}\pi$ and find the value of $k$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Sketch one full cosine cycle that begins and ends at a negative value

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