Solving simple trigonometric equations in 0 ≤ θ ≤ 2π, equations that factorise or reduce to quadratics using identities, and graphical interpretation.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
“Find all x between 0 and 2π with 2 sin x = 1.” Two answers, not one — and a checklist that finds them every time.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Slide the line y = k across the graph and read off the solutions.
Copy these into your notebook in your own words — that is how they stick.
Isolate → principal value → CAST → all solutions in range.
Ignore the sign to find the acute angle; use CAST for the quadrants.
Factorise instead of dividing by sin x or cos x.
Convert to ONE function: sin²x = 1 − cos²x, sin 2x = 2 sin x cos x, cos 2x = 1 − 2sin²x …
|sin x| > 1 or |cos x| > 1 has no solution.
For sin kx on 0 ≤ x ≤ 2π search 0 ≤ kx ≤ 2kπ.
Solutions are x-coordinates where the graph meets the line y = constant (or another curve).
Radians unless degrees are specified.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (26 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [13 marks]
Solve each equation for 0 ≤ x ≤ 2π, giving exact answers in terms of π unless stated otherwise.
(a) 2 sin x = 1 [3]
(b) 2cos²x − cos x − 1 = 0 [5]
(c) sin 2x = cos x [5]
Question 2 [13 marks]
Solve each equation for 0 ≤ x ≤ 2π.
(a) 2sin²x + 3cos x = 0 [6]
(b) tan x = 2, giving answers in radians to 3 decimal places. [3]
(c) sin 2x = cos 2x [4]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.