1 - 90° - 6 90° 180° 270° 360° x y - 180° - 270° - 360° - 4 - 2 0 2 The diagram shows the graph of sin y a b x c = + for , x 360 360 ° ° G G - where a, b and c are integers. (a) Write down the period of . sin a b x c + [1] (b) Find the value of a, of b and of c. [3]

1(a) o 1080 B1 1(b) 4 = a B1 3 = b B1 2 = − c B1

3 Solve the equation cosec cot cot 2 2 9 2 2 i i i + = + , where i is in radians and r r 2 2 1 1 i - . [5]

3 ( ) 2 2 cot 1 2cot 2cot 9 θ θ θ + + = + B1 For use of correct identity ( )( ) 3cot 4 cot 2 0 θ θ + − = 4 cot , cot 2 3 θ θ = − = M1 For attempt to solve their quadratic in cotθ to obtain cotθ = k 3 1 tan , tan 4 2 θ θ = − = M1 For dealing with cotθ = k correctly to get 1 tanθ = k 0.644 θ = − A1 0.464 θ = A1 To earn marks, you must first use the identity relating cosec²θ and cot²θ. Then, you need to solve the resulting quadratic equation for cotθ, and finally convert your cotθ values to tanθ to find the two correct angles in radians.

3 Solve the equation cot x 2 3 3 1 2 r - = b l , where x is in radians and x 0 1 G r. [5]

3 π tan 2 3 3   − = ±     x soi or π 3 sin 2 3 2   − = ±     x soi B1 B0 if negative root is rejected Allow truncated decimals May be implied by subsequent work From use of 2 2 π π cosec 2 1 cot 2 3 3     − − = −         x x π π π 2π 4π 2 , , , 3 3 3 3 3 x − = − 2π 5π 2 0, , π, 3 3 x = π π 5π 0, , , 3 2 6 x = or 0, 1.05, 1.57, 2.62 or greater accuracy 4 M1 for correct order of operations to obtain one solution in the range using π tan 2 3   − =     x k or π sin 2 , 1 3   − = <     x m m Dep M1 for correct order of operations to obtain a second solution in the range using ( ) 1 π 2 tan π 3 −   − = ±     x k or ( ) 1 π 2 π sin , 1 3 −   − = − <     x m m oe ( ) 1 π 2 sin , 1 3 −   − = − <     x m m oe A1 for any pair of correct solutions A1 for remaining pair of solutions, with no extra solutions within the range To earn marks, you must first correctly transform the given cotangent equation into a tangent or sine equation, allowing for positive or negative roots. Then, use the correct order of operations to find at least one solution within the given range, followed by a second solution using the appropriate periodicity or symmetry. Finally, provide two pairs of correct solutions, ensuring no extra solutions are included within the specified range.

4 Solve the equation , cot x 2 3 3 0 r + - = b l where x 1 1 r r - radians. Give your answers in terms of r. [4]

4 π 1 tan 2 3 3   + =     x B1 7 5 11 , , , 12 12 12 12 π π π π = − − x 3 M1 for using correct order of operations A1 for two correct solutions A1 for two further correct solutions and no other solutions in range You earn the first mark by correctly rewriting the cotangent equation in terms of tangent. The next mark is for correctly using the order of operations to find the principal values for x. The final two marks are for finding all four correct solutions for x within the given range, expressed in terms of pi, and not including any extra solutions.

Cambridge IGCSE Additional Mathematics · 0606

IGCSE Additional Mathematics (0606) Trigonometry past paper questions

These questions cover trigonometric identities, equations, and graphs across the full range — the identities that make later calculus tractable.

121 free questions from 2016–2021, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.

Trigonometry in IGCSE Additional Mathematics 0606 exams, 2020–2025

Across 2020–2025, Trigonometry accounted for 132 questions worth 940 marks in Cambridge IGCSE Additional Mathematics (0606) papers.

By year
Year	Questions	Marks
2020	19	145
2021	18	122
2022	23	166
2023	24	169
2024	29	213
2025	19	125

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Solving trigonometric equation588 marks
Trigonometric Identity384 marks
Six trigonometric functions and special angles261 marks

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2021 Oct/Nov · Paper 1 · Q1 · 4 marks
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2021 Feb/Mar · Paper 1 · Q2 · 3 marks
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2021 May/Jun · Paper 1 · Q3 · 5 marks
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2021 Oct/Nov · Paper 1 · Q3 · 5 marks
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2021 Oct/Nov · Paper 1 · Q4 · 4 marks
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Trigonometry in IGCSE Additional Mathematics 0606 exams, 2020–2025

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