WJEC Unit 3 2024 June — Question 12

Exam BoardWJEC
ModuleUnit 3 (Unit 3)
Year2024
SessionJune
TopicSmall angle approximation

12. (a) Given that \(\theta\) is small, show that \(2 \cos \theta + \sin \theta - 1 \approx 1 + \theta - \theta ^ { 2 }\).
(b) Hence, when \(\theta\) is small, show that $$\frac { 1 } { 2 \cos \theta + \sin \theta - 1 } \approx 1 + a \theta + b \theta ^ { 2 }$$ where \(a , b\) are constants to be found.
\includegraphics[max width=\textwidth, alt={}, center]{e4a4ea5b-7278-4735-925c-265a556ad679-25_2382_1837_278_178}