SPM 2023 Add Maths Paper 1, Question 15Trigonometric Functions

Solved on video in English and Bahasa Melayu · Form 5, Trigonometric Functions · 6:21 video

The question

(a)

Table 1 shows the values of x for the equation y + 3 sin(3/2 x) = 1. (a) Complete the values of y in Table 1. The x-values (in radians) are: 0, π/6, π/3, π/2, 2π/3, 5π/6, π, 7π/6, 4π/3, 3π/2, 5π/3, 11π/6, 2π.

(b)

Using a scale of 3 cm to π/3 on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of y + 3 sin(3/2 x) = 1 for 0 ≤ x ≤ 2π.

(c)(i)

(c)(i) State an equation of a suitable straight line to solve 3 sin(3/2 x) = 4x/π − 2.

(c)(ii)

(c)(ii) Hence, on the graph in (b), draw the straight line y = −4x/π + 3 to solve 3 sin(3/2 x) = 4x/π − 2. State the value of x in terms of π.

SPM 2023 Add Maths Paper 1, Question 15: the question as drawn in Eduly's video6:21

Part (a)

Step 1

Rearrange the equation: y = 1 − 3 sin(3/2 x), with x in radians.

Why this step

We need y alone so each x-value is a single substitution. Moving 3 sin(3/2 x) across flips its sign, so y = 1 − 3 sin(3/2 x).

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

Final answer

y = 1.00, −1.12, −2.00, −1.12, 1.00, 3.12, 4.00, 3.12, 1.00, −1.12, −2.00, −1.12, 1.00

Where students lose marks

Watch out: the x-values are in radians. Set your calculator to radian mode, not degrees, or every y-value will be wrong.

Part (b)

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

Final answer

Graph (see video)

Where students lose marks

Watch out: plot all 13 points from the table and use the given scales, then draw a smooth curve.

Part (c)(i)

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

Final answer

y = −4x/π + 3

Where students lose marks

Watch out: the sine term is 1 − y, not y − 1. Sign slips give wrong lines like y = 4x/π − 1.

Part (c)(ii)

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

Final answer

x ≈ 19π/30 (≈ 0.63π)

Where students lose marks

Watch out: a wrong line from (c)(i) gives a wrong intersection, e.g. 10π/9. Draw y = 3 − 4x/π and read x carefully.

Watch every step of this question solved on video (6:21), with the reason behind each step and a box that checks your own answer.

Start 7 days freeAlready a member? Watch it now

No card. Every past-year question on video, in English and BM.

All questions in SPM 2023 Paper 1

Trigonometric Functions: lessons and every past-year question

Baca dalam Bahasa Melayu

More Trigonometric Functions questions

Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.