The first two terms of an arithmetic progression are $\tan \theta$ and $\sin \theta$, respectively, where $0 < \theta < \frac{1}{2}\pi$.
(a)[4]
With $\theta = \frac{1}{4}\pi$ given, find the exact total of the first $40$ terms of the progression.
(b(i))[2]
Find the sum to infinity of the progression in terms of $\theta$.
(b(ii))[3]
With $\theta = \frac{1}{3}\pi$ given, find the total of the first $10$ terms of the progression. Give your answer to $3$ significant figures.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Finds the common difference $d=\sin\theta-\tan\theta$” …