Given that θ \theta\,θ is small, use the small angle approximation of cosθ \cos \theta\,cosθ to show that
4cos(θ)+cos2(2θ)≈5−6θ2+4θ4 4 \cos(\theta) + \cos^2(2\theta) \approx 5 - 6\theta^2 + 4\theta^4 4cos(θ)+cos2(2θ)≈5−6θ2+4θ4Hence find an approximation of 4cos(θ)+cos2(2θ)4 \cos(\theta) + \cos^2(2\theta)4cos(θ)+cos2(2θ) when θ=3∘\theta = 3^\circθ=3∘
Calculate the percentage error in your approximation
Practise Edexcel A Level Maths Radians with exam-style questions for A Level Maths. 52 questions covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations, matched to the Edexcel A Level Maths (9MA0) 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.