18M.1.AHL.TZ1.H_2

pestleMathematicsAIHLPaper 118M· sl-5-3-differentiating-polynomials-n-e-zsource ↗

Let $y = {\text{si}}{{\text{n}}^2}\theta ,\,\,0 \leqslant \theta \leqslant \pi$ .

Find $\frac{{{\text{d}}y}}{{{\text{d}}\theta }}$

[2]

Hence find the values of θ for which $\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2y$ .

[5]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt at chain rule or product rule (M1)

$\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta$ A1

[2 marks]

$2\,{\text{sin}}\,\theta \,{\text{cos}}\,\theta = 2{\text{si}}{{\text{n}}^2}\theta$

sin θ = 0 (A1)

θ = 0, $\pi$ A1

obtaining cos θ = sin θ (M1)

tan θ = 1 (M1)

$\theta = \frac{\pi }{4}$ A1

[5 marks]

Examiners’ report

[N/A]