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1.8 E: Trigonometry

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Question 20

It is given that

f(x)=3x3+4x2+13x+4f(x) = 3x^3 + 4x^2 + 13x + 4f(x)=3x3+4x2+13x+4

a.

Show that (3x+1)(3x + 1)(3x+1) is a factor of f(x)f(x)f(x).

[2]
b.

Factorise f(x)f(x)f(x) completely.

[2]
c.

Prove that the equation

3sec⁡2θ+4sec⁡θ+13+4cos⁡θ=03\sec^2\theta + 4\sec\theta + 13 + 4\cos\theta = 03sec2θ+4secθ+13+4cosθ=0

has no real solutions.

[4]
Markscheme

1.8 E: Trigonometry Questions

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

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank