SPM 2023 Add Maths Paper 2, Question 4Trigonometric Functions

Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 7:49 video

The question

(a)

Diagram 2 shows the graph of y = tan x + c for 0 ≤ x ≤ p, where c and p are constants. The curve passes through the point (p, −2). State the value of c and of p.

(b)(i)

For the following question, give your answer in the simplest fraction form in terms of π radians.

(b)(i) Solve the equation 2 cos x = −1 for π ≤ x ≤ 3π.

(b)(ii)

(b)(ii) Sketch the graph of y = 2 cos x for 0 ≤ x ≤ 2π. By drawing a suitable straight line on your sketch, find the range of values of x for which cos x < −1/2 for 0 ≤ x ≤ 2π.

SPM 2023 Add Maths Paper 2, Question 4: the question as drawn in Eduly's video7:49

Part (a)

Step 1

At x = 0, y = tan 0 + c = c. From the graph the y-intercept is −1, so c = −1.

Why this step

Since tan 0 = 0, putting x = 0 leaves just c. So the y-intercept you read off the graph is directly the value of c.

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

Final answer

c = −1, p = 7π/4

Where students lose marks

Watch out: your calculator gives −45° for tan^(−1)(−1). Use the graph to place the angle in the correct quadrant, so p = 7π/4.

Part (b)(i)

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

Final answer

x = 4π/3 or x = 8π/3

Where students lose marks

Watch out: after finding π/3, list every solution, then reject any outside π ≤ x ≤ 3π. Give answers as fractions of π.

Part (b)(ii)

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

Final answer

2π/3 < x < 4π/3

Where students lose marks

Watch out: use a ruler, amplitude 2, and the line y = −1 (not y = −1/2), since the curve is 2 cos x.

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