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1.8 E: Trigonometry

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Question 96

Let f(x)=6sin⁡xcos⁡x+6cos⁡2x−1f(x) = 6 \sin x \cos x + 6 \cos^2 x - 1f(x)=6sinxcosx+6cos2x−1.

a.

Write f(x)f(x)f(x) in the form

asin⁡2x+bcos⁡2x+c a \sin 2x + b \cos 2x + c asin2x+bcos2x+c

where a,b,a, b,a,b, and ccc are integers to be found.

[3]
b.

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

Rsin⁡(2x+α)+c R \sin (2x + \alpha) + c Rsin(2x+α)+c

where R>0R > 0R>0 and 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of RRR and give the value of α\alphaα in radians to 3 significant figures.

[3]
c.

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

[3]

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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