Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

We are told that $a = \sin \theta - 3 \cos \theta$ and $b = 3 \sin \theta + \cos \theta$, where $0^\circ \leq \theta \leq 360^\circ$.

(i)[3]

Show that $a^2 + b^2$ remains unchanged for every value of $\theta$.

(ii)[4]

Find the values of $\theta$ for which $2a = b$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Squares $a$ and $b$ accurately” …