Solve equation using small angle approximation

A question is this type if and only if it requires finding an approximate numerical solution to an equation by first applying small angle approximations to simplify the equation.

3 questions · Standard +0.3

Sort by: Default | Easiest first | Hardest first
OCR H240/02 2018 September Q3
4 marks Standard +0.3
3 Use small angle approximations to estimate the solution of the equation \(\frac { \cos \frac { 1 } { 2 } \theta } { 1 + \sin \theta } = 0.825\), if \(\theta\) is small enough to neglect terms in \(\theta ^ { 3 }\) or above.
WJEC Unit 3 2018 June Q7
3 marks Standard +0.3
Use small angle approximations to find the small negative root of the equation $$\sin x + \cos x = 0.5.$$ [3]
SPS SPS SM Pure 2021 May Q1
5 marks Standard +0.3
  1. For a small angle \(\theta\), where \(\theta\) is in radians, show that \(2\cos\theta + (1 - \tan\theta)^2 \approx 3 - 2\theta\). [3]
  2. Hence determine an approximate solution to \(2\cos\theta + (1 - \tan\theta)^2 = 28\sin\theta\). [2]