Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

(a(i))[3]

Express $\dfrac{\tan^2 \theta - 1}{\tan^2 \theta + 1}$ as $a\sin^2 \theta + b$, with $a$ and $b$ as the constants to determine.

(a(ii))[2]

Solve $\dfrac{\tan^2 \theta - 1}{\tan^2 \theta + 1} = \dfrac{1}{4}$ for $-90^\circ \leq \theta \leq 0^\circ$, showing all necessary working and, if helpful, using the earlier result.

(b(i))[2]

Find the $x$-coordinate for $A$.

(b(ii))[2]

Find the $y$-coordinate for $B$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate algebraic handling of $\frac{\tan^2\theta-1}{\tan^2\theta+1}$

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