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7.4 Simplifying a cos x +- b sin x

Question 1

Let $f(x) = 6 \sin x \cos x + 6 \cos^2 x - 1$ .

Write $f (x)$ in the form

\sin 2x + b \cos 2x + c

where $a, b,$ and $c$ are integers to be found.

[3]

Use the answer to part (a) to write $f (x)$ in the form

\sin (2x + \alpha) + c

where $R > 0$ and $\alpha < \frac{\pi}{2}$ . Give the exact value of $R$ and give the value of $α\alpha$ in radians to 3 significant figures.

[3]

Hence, or otherwise, (i) state the maximum value of $f (x)$ , (ii) find the second smallest positive value of $x$ at which a maximum value of $f (x)$ occurs. Give your answer to 3 significant figures.

[3]

Markscheme

7.4 Simplifying a cos x +- b sin x Questions

A Level
Maths
7.4 Simplifying a cos x +- b sin x

19 exam-style questions on Edexcel A Level Maths 7.4 Simplifying a cos x +- b sin x. Each one has a worked solution and a mark scheme showing where the marks go.

7.4 Simplifying a cos x +- b sin x

Question bank

7.4 Simplifying a cos x +- b sin x

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Question 1

Let $f(x) = 6 \sin x \cos x + 6 \cos^2 x - 1$ .

Write $f (x)$ in the form

\sin 2x + b \cos 2x + c

where $a, b,$ and $c$ are integers to be found.

[3]

Use the answer to part (a) to write $f (x)$ in the form

\sin (2x + \alpha) + c

where $R > 0$ and $\alpha < \frac{\pi}{2}$ . Give the exact value of $R$ and give the value of $α\alpha$ in radians to 3 significant figures.

[3]

Markscheme

7.4 Simplifying a cos x +- b sin x Questions

A Level
Maths
7.4 Simplifying a cos x +- b sin x

19 exam-style questions on Edexcel A Level Maths 7.4 Simplifying a cos x +- b sin x. Each one has a worked solution and a mark scheme showing where the marks go.