CAIE A-Level Mathematics 2.3 Trigonometry Question Bank

CAIE A-Level Mathematics 2.3 Trigonometry Question Bank
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise reciprocal trigonometric functions, identities and R-formula transformations to solve equations and retain every valid angle inside specified degree or radian intervals.

Exam points

  • replace sec, cosec and cot with reciprocal or quotient forms and apply their identities
  • express a sin x + b cos x as R sin(x ± α) or R cos(x ± α) with correct quadrant
  • solve the reduced equation and keep all solutions lying in the specified interval

Covered syllabus points

2.3.1—Reciprocal trig functions2.3.2—Trig identities

Question 4

[Maximum number: 5]

Solve the equation cot⁡θtan⁡(θ+45∘)=7\cot \theta \tan \left(\theta+45^{\circ}\right)=7 for 0∘<θ<90∘0^{\circ}<\theta<90^{\circ}.

Question 6

[Maximum number: 6]

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}.

Question 6(a)

(a)

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

[ 2 ]

Question 6(b)

(b)

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

[ 2 ]

Question 6(c)

(c)

Find the exact value of cos⁡2θ\cos 2 \theta.

[ 2 ]