Sine, cosine and tangent of any angle, exact values for π/6, π/4, π/3 and π/2 and their related angles, and the graphs of sin kx, cos kx and tan kx.
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.
Sine and cosine are just coordinates on the unit circle. Once you see that, signs, symmetries and graphs all fall into place.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Turn the point and watch the sine, cosine or tangent graph; or see them in 3D.
Copy these into your notebook in your own words — that is how they stick.
P(θ) = (cos θ, sin θ); tan θ = sin θ/cos θ.
I all; II sin; III tan; IV cos.
π/6: ½, √3/2, 1/√3; π/4: √2/2, √2/2, 1; π/3: √3/2, ½, √3.
Reference angle + CAST sign.
cos(−θ) = cos θ; sin(−θ) = −sin θ; tan(−θ) = −tan θ.
sin, cos: amplitude 1, period 2π. tan: period π, asymptotes at odd multiples of π/2.
Period 2π/k; amplitude unchanged. A sin kx: amplitude |A|.
Mark the key points at multiples of π/2 and the maximum/minimum values.
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 (20 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [11 marks]
Answer all parts. Give exact values where possible.
(a) Write down the exact values of (i) sin 2π/3 (ii) cos 5π/6 (iii) tan 7π/4. [3]
(b) State the amplitude and period of y = 3 sin 2x. [2]
(c) Sketch the graph of y = sin 2x for 0 ≤ x ≤ 2π. (Check: two complete cycles; zeros at 0, π/2, π, 3π/2, 2π; maxima 1 at π/4, 5π/4; minima −1 at 3π/4, 7π/4.) [4]
(d) State the number of solutions of sin 2x = 0.5 in the interval 0 ≤ x ≤ 2π. [2]
Question 2 [9 marks]
Answer all parts.
(a) Complete a table of values for y = cos 2x at x = 0, π/4, π/2, 3π/4, π. [2]
(b) State the range and the period of y = 2 cos x. [2]
(c) Using the graphs of y = sin x and y = cos x for 0 ≤ x ≤ 2π, find the values of x for which sin x = cos x. [3]
(d) Explain why tan x is not defined at x = π/2. [2]
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.