Given that θ \theta\,θ is small, use the small angle approximation of cosθ \cos \theta\,cosθ to show that
5cos(θ)−cos2(2θ)≈4+1.5θ2−4θ4 5 \cos(\theta) - \cos^2(2\theta) \approx 4 + 1.5\theta^2 - 4\theta^4 5cos(θ)−cos2(2θ)≈4+1.5θ2−4θ4Hence find an approximation of 5cos(θ)−cos2(2θ)5 \cos(\theta) - \cos^2(2\theta)5cos(θ)−cos2(2θ) when θ=2∘\theta = 2^\circθ=2∘
Calculate the percentage error in your approximation
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.