The Pythagorean identity, tan θ = sin θ/cos θ, the compound-angle and double-angle formulae, exact values from them, and proving identities.
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.
sin(A + B) is not sin A + sin B — it has its own formula. Learn the handful of identities and you can simplify, evaluate and prove almost anything in trigonometry.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
cos²θ + sin²θ ≡ 1; 1 + tan²θ ≡ sec²θ.
tan θ ≡ sin θ/cos θ.
sin(A ± B) = sinAcosB ± cosAsinB; cos(A ± B) = cosAcosB ∓ sinAsinB; tan(A ± B) = (tanA ± tanB)/(1 ∓ tanAtanB).
sin 2A = 2sinAcosA; cos 2A = cos²A − sin²A = 2cos²A − 1 = 1 − 2sin²A; tan 2A = 2tanA/(1 − tan²A).
Recognise sinAcosB − cosAsinB as sin(A − B).
One side only; end exactly at the other side.
75° = 45° + 30°; 15° = 45° − 30°.
You need not prove the compound-angle formulae.
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 (24 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [13 marks]
Answer all parts.
(a) Prove that (1 − cos 2x)/sin 2x ≡ tan x. [4]
(b) Given that sin A = 3/5 and cos B = 5/13, where A and B are acute angles, find the exact value of (i) sin(A + B), (ii) cos(A − B). [6]
(c) Find the exact value of cos 15°, using cos 15° = cos(45° − 30°). [3]
Question 2 [11 marks]
Answer all parts.
(a) Prove that sin x/(1 − cos x) ≡ (1 + cos x)/sin x. [4]
(b) Given tan A = 1/2 and tan B = 1/3, show that A + B = 45°. [3]
(c) Given that cos x = 4/5 and x is acute, find the values of sin 2x, cos 2x and tan 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.