Given that θ \theta\,θ is small, use the small angle approximation of cosθ \cos \theta\,cosθ to show that
2cos(θ)+cos2(2θ)≈3−5θ2+4θ4 2 \cos(\theta) + \cos^2(2\theta) \approx 3 - 5\theta^2 + 4\theta^4 2cos(θ)+cos2(2θ)≈3−5θ2+4θ4Hence find an approximation of 2cos(θ)+cos2(2θ)2 \cos(\theta) + \cos^2(2\theta)2cos(θ)+cos2(2θ) when θ=2∘\theta = 2^\circθ=2∘
Calculate the percentage error in your approximation
278 exam-style questions on Edexcel A Level Maths Radians, 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. Each one has a worked solution and a mark scheme showing where the marks go.