Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

The curve is given by $y = 3\cos 2x + 2$ for $0 \leq x \leq \pi$.
(a)[2]

Give the largest and smallest values of $y$.

(b)[2]

Sketch the graph of $y = 3\cos 2x + 2$ on $0 \leq x \leq \pi$.

(c(i))[1]

Using the straight line $y = kx$, where $k$ is a constant, state how many solutions the equation $3\cos 2x + 2 = kx$ has for $0 \leq x \leq \pi$ when $k = -3$.

(c(ii))[1]

Using the straight line $y = kx$, where $k$ is a constant, state how many solutions the equation $3\cos 2x + 2 = kx$ has for $0 \leq x \leq \pi$ when $k = 1$.

(c(iii))[1]

Using the straight line $y = kx$, where $k$ is a constant, state how many solutions the equation $3\cos 2x + 2 = kx$ has for $0 \leq x \leq \pi$ when $k = 3$.

(c)

Using the straight line $y = kx$, where $k$ is a constant, state how many solutions the equation $3\cos 2x + 2 = kx$ has for $0 \leq x \leq \pi$ in each case below.

(d)[2]

Fully describe a sequence of transformations that takes the graph of $y = f(x)$ to $y = g(x)$.

(e)[2]

Fully describe a sequence of transformations that takes the graph of $y = f(x)$ to $y = h(x)$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct values are $5$ and $-1$.

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