Selangor Trial 2025 Add Maths Paper 2, Question 5Trigonometric Functions

Solved on video in English · Form 5, Trigonometric Functions · 8:24 video

The question

(a)

(a) Prove that cosec 2A = ½ sec A cosec A.

(b)(i)

(b) Given that sin A = −4/5 and cos B = −1/√3, such that A and B are in the same quadrant. (i) Find sin B.

(b)(ii)

(b)(ii) Find cos(A + B).

(c)(i)

(c)(i) Sketch the graph of y = |2 + 5 sin 3x| for 0 ≤ x ≤ π.

(c)(ii)

(c)(ii) There are 6 solutions when y = m, such that m is a constant. State the range of values of m.

Selangor Trial 2025 Add Maths Paper 2, Question 5: the question as drawn in Eduly's video8:24

Part (a)

Step 1

Start from the left side and use the double-angle identity sin 2A = 2 sin A cos A.

Why this step

The target has only A, not 2A, so we replace sin 2A by 2 sin A cos A. Keep the cos A: sin 2A is not 2 sin A.

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

Final answer

Proved

Where students lose marks

Watch out: sin 2A = 2 sin A cos A, not 2 sin A. Then spot 1/cos A = sec A and 1/sin A = cosec A.

Part (b)(i)

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

Final answer

sin B = −√6/3

Where students lose marks

Watch out: B is in quadrant III, so sin B is negative. Take −√6/3, not +√6/3, and rationalise √(2/3).

Part (b)(ii)

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

Final answer

cos(A + B) = (3√3 − 4√6)/15

Where students lose marks

Watch out: cos A is negative in quadrant III, and cos(A + B) has a minus between the products. Rationalise before combining over 15.

Part (c)(i)

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

Final answer

Sketch (see video)

Where students lose marks

Watch out: translate up by 2, draw 3/2 cycles (not 1), and reflect the part below the x-axis upward for the modulus.

Part (c)(ii)

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

Final answer

2 ≤ m < 3

Where students lose marks

Don't overlook the reflected middle hump: m = 3 only touches its peak (5 solutions), so 3 is excluded but 2 is included.

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