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1.8 E: Trigonometry

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Question 65

The intensity, I I\,I units, of polarised light passing through a rotating filter is modelled by

I=I0cos⁡2θI = I_0 \cos^2\thetaI=I0​cos2θ

where I0 I_0\,I0​ is the maximum intensity and θ \theta\,θ is the angle of the filter in radians.

In one experiment the maximum intensity is measured as I0=12I_0 = 12I0​=12 units.

a.

Determine all the values of θ \theta\,θ in the interval 0≤θ≤2π 0 \leq \theta \leq 2\pi\,0≤θ≤2π for which I=9I = 9I=9 units. Give your answers as exact multiples of π\piπ.

[4]
b.

State the values of θ \theta\,θ in the interval 0≤θ≤2π 0 \leq \theta \leq 2\pi\,0≤θ≤2π at which the model predicts the maximum intensity.

[2]
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.

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