Free Trig equations & graphs questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Geometry & trigonometry. Each question has the answer and the marking points an examiner would look for.
Generate a full Trig Equations & Graphs worksheet →All Geometry & trigonometry questionsSolve the equation sin 2x = cos x for 0 ≤ x ≤ 2π.
| Part | Answer and marking points | Marks |
|---|---|---|
| x = π6, π2, 5π6, 3π2 use of a double-angle identity M1 cos x(2sin x − 1) = 0 A1 cos x = 0 or sin x = 12 A1 attempt to find all solutions in the interval (M1) x = π6, π2, 5π6, 3π2 A2 award A1 for at least half of the solutions; do not divide by cos x or sin x (solutions lost) | 6 |
Consider the equation 3sin(2x) + 1 = k, for 0 ≤ x ≤ π.
Find the set of values of k for which the equation has exactly two solutions.
| Part | Answer and marking points | Marks |
|---|---|---|
| −2 < k < 1, 1 < k < 4 sketch of y = 3sin(2x) + 1 over one full period M1 range from −2 to 4 A1 k = 1 gives three solutions (x = 0, π2, π) R1 k = 4 or k = −2 gives one solution R1 −2 < k < 1 or 1 < k < 4 A1 | 5 |
The height h metres of a seat on a Ferris wheel above the ground, t minutes after the ride starts, is h(t) = 35 − 25cos(π12t), t ≥ 0.
Write down the maximum height of the seat and the time for one full revolution.
Find the height of the seat after 2 minutes.
Find the length of time during one revolution for which the seat is more than 41 m above the ground.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 60 m; 24 minutes 60 m A1 24 minutes A1 | 2 |
| (b) | 13.3 m h(2) = 35 − 25cos(π6) (M1) 13.3 m A1 | 2 |
| (c) | 10.1 minutes 35 − 25cos(π12t) = 41 (M1) t = 6.93, t = 17.1 (A1)(A1) 10.1 minutes A1 | 4 |
Solve the equation cos 2x + 3sin x = 2 for 0 ≤ x ≤ 2π.
| Part | Answer and marking points | Marks |
|---|---|---|
| x = π6, π2, 5π6 use of a double-angle identity M1 (2sin x − 1)(sin x − 1) = 0 A1 sin x = 1 or sin x = 12 A1 attempt to find all solutions in the interval (M1) x = π6, π2, 5π6 A2 award A1 for at least half of the solutions; do not divide by cos x or sin x (solutions lost) | 6 |
Consider the equation 5sin(2x) + 1 = k, for 0 ≤ x ≤ π.
Find the set of values of k for which the equation has exactly two solutions.
| Part | Answer and marking points | Marks |
|---|---|---|
| −4 < k < 1, 1 < k < 6 sketch of y = 5sin(2x) + 1 over one full period M1 range from −4 to 6 A1 k = 1 gives three solutions (x = 0, π2, π) R1 k = 6 or k = −4 gives one solution R1 −4 < k < 1 or 1 < k < 6 A1 | 5 |
The height h metres of a seat on a Ferris wheel above the ground, t minutes after the ride starts, is h(t) = 24 − 15cos(π12t), t ≥ 0.
Write down the maximum height of the seat and the time for one full revolution.
Find the height of the seat after 5 minutes.
Find the length of time during one revolution for which the seat is more than 28 m above the ground.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 39 m; 24 minutes 39 m A1 24 minutes A1 | 2 |
| (b) | 20.1 m h(5) = 24 − 15cos(5π12) (M1) 20.1 m A1 | 2 |
| (c) | 9.94 minutes 24 − 15cos(π12t) = 28 (M1) t = 7.03, t = 17.0 (A1)(A1) 9.94 minutes A1 | 4 |
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in