SPM 2019 Add Maths Paper 1, Question 21Trigonometric Functions

Solved on video in English · 3 marks · Form 5, Trigonometric Functions · 4:15 video

The question

Diagram 8 shows the graph of y = |n sin(alpha) cos(alpha)| for 0 <= alpha <= 2*pi. (a) Express m in terms of n. (b) There are 8 solutions when y=k, where k is a constant. State the range of k in terms of m.

[3 marks]

SPM 2019 Add Maths Paper 1, Question 21: the question as drawn in Eduly's video4:15

Step 1

Use the double angle identity sin(2alpha) = 2 sin(alpha)cos(alpha), so sin(alpha)cos(alpha) = (1/2) sin(2alpha).

Why this step

sin α cos α is a product of two waves, which is hard to read. Writing it as one sin 2α lets us spot the maximum straight away.

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

Final answer

(a) m = n/2; (b) 0 < k < m

Where students lose marks

Watch out: the modulus flips the negative halves upward, so count all 4 humps and 2 crossings per hump.

Watch every step of this question solved on video (4:15), with the reason behind each step and a box that checks your own answer.

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