SPM 2017 Add Maths Paper 2, Question 10Trigonometric Functions

Solved on video in English and Bahasa Melayu · 10 marks · Form 5, Trigonometric Functions · 6:42 video

The question

(a) Prove that 2 tanθ cos²θ = sin 2θ. (b) Hence, solve the equation 4 tanθ cos²θ = 1 for 0 ≤ θ ≤ 2π. (c)(i) Sketch the graph of y = sin 2θ for 0 ≤ θ ≤ 2π. (ii) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation 4π tanθ cos²θ = x - 2π for 0 ≤ θ ≤ 2π. State the number of solutions.

[10 marks]

SPM 2017 Add Maths Paper 2, Question 10: the question as drawn in Eduly's video6:42

Step 1

LHS = 2 tanθ cos²θ = 2(sinθ/cosθ)cos²θ = 2 sinθ cosθ = sin 2θ = RHS. Proven.

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

Final answer

(a) Shown; (b) θ = π/12, 5π/12, 13π/12, 17π/12; (c) sketch (see video), 4 solutions

Where students lose marks

Watch out: 2θ runs to 4π, so part (b) has four roots, not two. In (c)(ii), draw the line from (0, -1) to (2π, 0) exactly.

Watch every step of this question solved on video (6:42), with the reason behind each step and a box that checks your own answer.

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