OCR H240/03 2017 Specimen — Question 4 4 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2017
SessionSpecimen
Marks4
TopicSmall angle approximation
TypeSimplify expression to polynomial form
DifficultyStandard +0.3 This is a straightforward small angle approximation question requiring substitution of cos θ ≈ 1 - θ²/2 and algebraic simplification. It's slightly easier than average as it's a 'show that' question with a clear target, requiring only standard technique application without problem-solving or insight.
Spec1.05e Small angle approximations: sin x ~ x, cos x ~ 1-x^2/2, tan x ~ x

For a small angle \(\theta\), where \(\theta\) is in radians, show that \(1 + \cos \theta - 3\cos^2 \theta \approx -1 + \frac{3}{2}\theta^2\). [4]

For a small angle $\theta$, where $\theta$ is in radians, show that $1 + \cos \theta - 3\cos^2 \theta \approx -1 + \frac{3}{2}\theta^2$. [4]

\hfill \mbox{\textit{OCR H240/03 2017 Q4 [4]}}