| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 6 |
| Topic | Standard trigonometric equations |
| Type | Product of trig functions |
| Difficulty | Challenging +1.2 This question requires converting tan²θ to sec²θ - 1, then substituting cos θ = 1/sec θ to obtain a cubic equation in cos θ, which factors or solves to give cos θ = 3/4. While it involves multiple trigonometric identities and algebraic manipulation across several steps, the techniques are standard A-level fare with no novel insight required. The 6 marks and multi-step nature place it moderately above average difficulty. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
Solve the following trigonometric equation in the range given.
$$4\tan^2\theta\cos\theta = 15, \quad 0 \leq \theta < 360°.$$
[6 marks]
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q9 [6]}}