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If the sum to infinity of the progression is $\frac{1}{2}$, determine the value of $\theta$. Write your answer in the form $\sin^{-1}k$, where $k$ is a rational number.
Mathematics 9709 · AS & A Level · Series
Series — practice question
The progression’s first two terms are $4\sin^2\theta$ and $8\sin^3\theta$, with $\theta$ an angle for which $0 < \theta \leq \frac{1}{6}\pi$.
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This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “An unsimplified correct expression for $r=\frac{8\sin^3\theta}{4\sin^2\theta}$, or $r=2\sin\theta” …
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