SPM 2021 Add Maths Paper 2, Question 5Trigonometric Functions

Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 6:31 video

The question

(a)

(a)(i) Prove that 2 cot²A sin²A = 1 + cos 2A. (a)(ii) Hence, solve the equation 2 cot²A sin²A = 1/2 for 0 ≤ A ≤ 2π, in terms of π.

(b)

(b) Sketch the graph of y = 1 + |3 cos (3/2)A| for 0 ≤ A ≤ 2π.

Step 1

LHS = 2 cot²A sin²A = 2 (cos²A / sin²A)(sin²A) = 2 cos²A.

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

Final answer

(i) Proved; (ii) A = π/3, 2π/3, 4π/3, 5π/3

Where students lose marks

Watch out: finish the proof at 1 + cos 2A, and list every angle over 0 ≤ 2A ≤ 4π before halving.

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

Final answer

Sketch (see video)

Where students lose marks

Watch out: take the modulus first, then translate up by 1. Lifting first gives the wrong graph.

Watch every step of this question solved on video (6:31), with the reason behind each step and a box that checks your own answer.

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