SPM 2018 Add Maths Paper 2, Question 7Trigonometric Functions

Solved on video in English and Bahasa Melayu · 10 marks · Form 5, Trigonometric Functions · 7:43 video

The question

(a) Prove sin(3x + π/6) − sin(3x − π/6) = cos 3x. (b) Hence, (i) solve the equation sin(3x/2 + π/6) − sin(3x/2 − π/6) = 1/2 for 0 ≤ x ≤ 2π and give your answer in the simplest fraction form in terms of π rad, (ii) sketch the graph of y = sin(3x + π/6) − sin(3x − π/6) − 1/2 for 0 ≤ x ≤ π.

[10 marks]

SPM 2018 Add Maths Paper 2, Question 7: the question as drawn in Eduly's video7:43

Step 1

Expand both terms with the compound-angle formula sin(A ± B) = sin A cos B ± cos A sin B, taking A = 3x and B = π/6.

9 more steps, each with the reason for it, in the full solution

Final answer

(a) Shown; (b)(i) x = 2π/9, 10π/9, 14π/9; (b)(ii) sketch of y = cos 3x − 1/2 (see video)

Where students lose marks

Watch out: in (b)(i), θ = 3x/2 runs up to 3π. Don't miss 7π/3, and multiply θ by 2/3 to get x.

Watch every step of this question solved on video (7:43), with the reason behind each step and a box that checks your own answer.

Start 7 days freeAlready a member? Watch it now

No card. Every past-year question on video, in English and BM.

All questions in SPM 2018 Paper 2

Trigonometric Functions: lessons and every past-year question

Baca dalam Bahasa Melayu

More Trigonometric Functions questions

Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.