Challenging +1.2 This question requires algebraic manipulation using the identity sin²θ = 1 - cos²θ to convert to harmonic form, then finding the minimum of a linear function in cos θ subject to the constraint -1 ≤ cos θ ≤ 1. While it involves multiple steps and careful algebraic work, the techniques are standard for Further Maths Pure content and the path is clearly signposted by the question itself. It's moderately harder than average due to the algebraic manipulation required and the need to consider domain restrictions, but doesn't require novel insight.
10.
By first showing that \(\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }\) can be expressed in the form \(p + q \cos \theta\), where \(p\) and \(q\) are integers, find the least possible value of \(\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }\).
State the exact value of \(\theta\), in radians in the interval \(0 \leqslant \theta < 2 \pi\), at which this least value occurs.
10.
By first showing that $\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }$ can be expressed in the form $p + q \cos \theta$, where $p$ and $q$ are integers, find the least possible value of $\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }$.
State the exact value of $\theta$, in radians in the interval $0 \leqslant \theta < 2 \pi$, at which this least value occurs.\\
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q10 [4]}}