MRSM Trial 2025 Add Maths Paper 1, Question 13Trigonometric Functions

Solved on video in English · Form 5, Trigonometric Functions · 5:55 video

The question

(a)

It is given that y = 3 cos 2x + 1. State (i) the amplitude, (ii) the period of the graph.

(b)

It is given that y = 3 cos 2x + 1.

(b)(i) Complete the values of y in Table 1 (x = 0°, 30°, 60°, 90°, 120°, 150°, 180°) and draw the graph of y = 3 cos 2x + 1 for 0° ≤ x ≤ 180°. (ii) Hence, using the same axes, draw a suitable graph to find the solutions to the equation 3x cos 2x = 360° − x for 0° ≤ x ≤ 180°, and state the solution.

MRSM Trial 2025 Add Maths Paper 1, Question 13: the question as drawn in Eduly's video5:55

Part (a)

Step 1

For y = a cos bx + c, the amplitude is |a| and the period is 360°/b (or 2π/b in radians).

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

Final answer

amplitude = 3, period = 180°

Where students lose marks

Watch out: the 2 in cos 2x halves the period to 180°, and the +1 does not change the amplitude.

Part (b)

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

Final answer

Table: 4, 2.5, −0.5, −2, −0.5, 2.5, 4; graph y = 360°/x; x ≈ 144° to 150°

Where students lose marks

Watch out: use degree mode, and draw y = 360°/x, not y = 360° − x.

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