SPM 2023 Add Maths Paper 1, Question 4Trigonometric Functions

Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 3:28 video

The question

(a)

Diagram 3 shows point A(−p, q) lying on the circumference of a unit circle, where p and q are positive. β is the acute angle between OA and the positive y-axis. Express tan β in terms of p and/or q. (a) tan β.

(b)

Using the same point A(−p, q) and angle β as part (a) (where tan β = p/q), express cot(180° + β) in terms of p and/or q. (b) cot(180° + β).

SPM 2023 Add Maths Paper 1, Question 4: the question as drawn in Eduly's video3:28

Part (a)

Step 1

In the right triangle formed by A(−p, q), the side opposite β (horizontal distance from the y-axis) is p and the side adjacent to β (vertical distance) is q.

Why this step

A side length is never negative. The minus in (−p, q) only tells us A is left of the y-axis, so the opposite side is p, not −p.

1 more step, with the reason for it, in the full solution

Final answer

tan β = p/q

Where students lose marks

Watch out: β is acute, so tan β = p/q. Do not carry the minus from (−p, q) into the answer and write −p/q.

Part (b)

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

Final answer

cot(180° + β) = q/p

Where students lose marks

Watch out: carry over tan β = p/q from part (a), not −p/q, or your final answer will be wrong.

Watch every step of this question solved on video (3:28), with the reason behind each step and a box that checks your own answer.

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