SPM 2024 Add Maths Paper 2, Question 8Trigonometric Functions
Solved on video in English · Form 5, Trigonometric Functions · 7:00 video
The question
(a) (i) Prove that cos 2θ = cos²θ − sin²θ. (ii) Hence, solve the equation 3cos²θ = 2 + 3sin²θ for 180° ≤ θ ≤ 360°.
(b) (i) Sketch the graph of y = −|cos²θ − sin²θ| + 4/5 for 0 ≤ θ ≤ 2π. (ii) There are 8 solutions when y = h, such that h is a constant. State the range of values of h.
Step 1
LHS = cos 2θ = cos(θ + θ)
Why this step
Prove means start from the compound angle formula with 2θ = θ + θ. Quoting cos 2θ = 1 − 2sin²θ as a shortcut skips the required proof.
22 more steps, each with the reason for it, in the full solution
Final answer
(a)(i) Proved; (a)(ii) θ ≈ 204.10° or 335.91°; (b)(i) Sketch (see video); (b)(ii) −1/5 < h < 4/5
Where students lose marks
Watch out: double the range to 360° ≤ 2θ ≤ 720° in (a)(ii), and keep the modulus in (b), or h comes out wrong.
Watch every step of this question solved on video (7:00), 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.
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