CAIE A-Level Mathematics 3.3.1 Reciprocal trig functions

CAIE A-Level Mathematics 3.3.1 Reciprocal trig functions
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using sec, cosec and cot with their graphs, domains and reciprocal links to solve or justify trigonometric equations.

How this is tested

  • sketch y = cosec x with a comparison graph to justify how many roots occur

Question 6(d)

[Maximum number: 3]

The polynomials f(x) and g(x) are defined by

f(x)=4x3+ax2+8x+15 and g(x)=x2+bx+18\mathrm{f}(x)=4 x^{3}+a x^{2}+8 x+15 \quad \text { and } \quad \mathrm{g}(x)=x^{2}+b x+18

where a and b are constants.

Hence solve the equation f(cosec⁡θ)−g(cosec⁡θ)=0\mathrm{f}(\operatorname{cosec} \theta)-\mathrm{g}(\operatorname{cosec} \theta)=0 for 0<θ<2π0<\theta<2 \pi.