SPM 2020 Add Maths Paper 1, Question 19Trigonometric Functions

Solved on video in English and Bahasa Melayu · 6 marks · Form 5, Trigonometric Functions · 5:48 video

The question

(a)(i)

Diagram 9 shows the point R(-h, h) on a unit circle. The angle theta degrees is measured anticlockwise from the positive x-axis, sweeping one complete revolution (shown by the spiral at the origin) before stopping along OR in the second quadrant. State the value of theta.

[2 marks]

(a)(ii)

Express 2 sin(-theta) in terms of h.

[2 marks]

(b)

Given sin theta = p, where theta is an obtuse angle, express cos(30 degrees - theta) in terms of p. State your answer in simplest form.

[2 marks]

SPM 2020 Add Maths Paper 1, Question 19: the question as drawn in Eduly's video5:48

Part (a)(i)

Step 1

On the unit circle R = (cos theta, sin theta) = (-h, h), so cos theta = -h and sin theta = h; equivalently tan theta = h/h = 1, giving a reference (basic) angle of 45 degrees.

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

Final answer

θ = 495°

Where students lose marks

Watch out: 45° is only the basic angle. Place it in the second quadrant (135°), then add the full 360° turn shown in the diagram.

Part (a)(ii)

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

Final answer

2 sin(−θ) = −2h

Where students lose marks

Watch out: sin θ is just the y-coordinate of R, so sin θ = h. Do not write √(2h²).

Part (b)

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

Final answer

cos(30° − θ) = (p − √(3(1 − p²)))/2

Where students lose marks

Watch out: θ is obtuse, so cos θ is negative. Forgetting the minus sign in −√(1 − p²) makes the whole answer wrong.

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