CAIE A-Level Mathematics 1.5.2 Exact trig values

CAIE A-Level Mathematics 1.5.2 Exact trig values
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using exact trig values for 30°, 45°, 60° and related angles to keep answers in exact surd or fractional form.

How this is tested

  • use exact sin, cos or tan values for related angles instead of decimal approximations

Question 3(a)

[Maximum number: 3]

The function f is defined by f(x)=tan⁡2(12x)\mathrm{f}(x)=\tan ^{2}\left(\frac{1}{2} x\right) for 0⩽x<π0 \leqslant x<\pi.

Find the exact value of f′(23π)\mathrm{f}^{\prime}\left(\frac{2}{3} \pi\right).