SPM 2024 Add Maths Paper 1, Question 8Trigonometric Functions
Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 4:04 video
The question
It is given that sin A = p/2 and sin(A + B) − sin(A − B) = 2p, such that A and B are acute angles. Express in terms of p: (a) cos A.
Express in terms of p: (b) sin B.
Part (a)
Step 1
Since sin A = p/2 and A is acute, construct a right triangle with opposite side = p and hypotenuse = 2.
Why this step
Sin is opposite ÷ hypotenuse, so p/2 gives two sides at once. Pythagoras then finds the third side and we can read off cos A.
2 more steps, each with the reason for it, in the full solution
Final answer
cos A = √(4 − p²) / 2
Where students lose marks
Watch out: √(4 − p²) does not simplify to 2 − p. Keep the whole surd, so cos A = √(4 − p²)/2.
Part (b)
5 more steps, each with the reason for it, in the full solution
Final answer
sin B = 2p / √(4 − p²)
Where students lose marks
Watch out: when subtracting sin(A − B), the minus sign changes both terms inside the bracket, not just the first.
Watch every step of this question solved on video (4:04), 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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