CAIE A-Level Mathematics 2.3.1 Reciprocal Trigonometric Functions

CAIE A-Level Mathematics 2.3.1 Reciprocal Trigonometric Functions
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise converting sec, cosec and cot to cosine, sine and tangent, applying reciprocal identities and selecting all valid solutions over positive or negative angle ranges.

How this is tested

  • replace sec θ, cosec θ or cot θ by its reciprocal or sine–cosine ratio
  • use identities such as cosec² θ = 1 + cot² θ to form a solvable quadratic
  • convert valid reciprocal values back to trig ratios and find every angle in the interval

Question 6(b)

[Maximum number: 2]

It is given that 3sin⁡2θ=cos⁡θ3 \sin 2 \theta=\cos \theta where θ\theta is an angle such that 0∘<θ<90∘0^{\circ}<\theta<90^{\circ}.

Find the exact value of sec⁡θ\sec \theta.