Standard +0.3 This question requires applying standard small angle approximations (sin θ ≈ θ, cos θ ≈ 1 - θ²/2) to simplify an equation, then solving a quadratic. It's slightly above average difficulty because students must correctly handle the half-angle (θ/2) and manipulate the resulting expression, but the technique is straightforward once the approximations are applied.
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.
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.
\hfill \mbox{\textit{OCR H240/02 2018 Q3 [4]}}