Maths with David

    9709. P3. TrigonometryPast exam questions

    9709/31/M/J/25q7 – Mark Scheme

    (a) Express 5sin(x+ \frac{1}{6} \pi) - 4cos x in the form Rsin(x - \alpha ) , where R>0 and 0 < \alpha < \frac{1}{2} \pi . State the exact value of R and give the value of \alpha correct to 3 decimal places. [4 marks]

    (b) Hence solve the equation 5sin ( 2 \theta + \frac{1}{6} \pi ) - 4cos2 \theta = \sqrt{7} for 0 \leq \theta \leq \pi . Give your answers correct to 2 decimal places. [4 marks]

    9709/32/M/J/25q4 – Mark Scheme

    Solve the equation 3cotx – 4cot2x = 3 for 0^{ \circ } \leq x \leq 180^{ \circ} [6 marks]

    9709/32/M/J/25q7 – Mark Scheme

    (a) Express 7 sin \theta + 24 cos \theta in the form Rcos( \theta - \alpha ) , where 0 < \alpha < \frac{1}{2} pi . Give the value of \alpha correct to 4 decimal places. [3 marks]

    (b) Hence solve the equation 7sin \frac{1}{3} x + 24cos \frac{1}{3} x = 24.5 for 0 < x < \pi [4 marks]

    9709/33/M/J/25q8 – Mark Scheme

    (a) Prove the identity cot^2 \theta - tan^2 \theta \equiv 4cot 2 \theta cosec 2 \theta . [4 marks]

    (b) Hence solve the equation cot^2x - tan^2x = 5 sec 2x for 0^{ \circ } < x < 90^{ \circ} . [4 marks]